Fortune smiled on Everton again as they took a point from the Premier League's bottom club on the back of a disjointed display in the rain at Selhurst Park.
The Blues made the worst possible start as James McArthur despatched Jordan Pickford's parry off Ruben Loftus-Cheek's shot into the empty net with just 50 seconds on the clock but were level just four minutes later from the penalty spot.
Wilfried Zaha restored the Eagles' lead later in the half but the home side shot themselves in the foot in stoppage time before the interval when Julian Speroni played Scott Dann into trouble and Oumar Niasse was sent clear to slide home a second equaliser.
Everton, who were better defensively and in midfield after half-time, almost took the lead through substitute Dominic Calvert-Lewin early in the second period but David Unsworth's men were generally poor going forward and rode their luck against Palace's set-piece threat at the other end.
Unsworth had kept faith with Gylfi Sigurdsson in the “number 10” position behind Niasse, leaving Wayne Rooney and Calvert-Lewin on the bench. Morgan Schneiderlin started alongside Idrissa Gueye but lasted just 45 minutes, Tom Davies's energy being preferred to the Frenchman's laid-back demeanour in the second half.
Michael Keane was preferred to Ashley Williams but the England defender was caught napping inside the first minute as he ushered Loftus-Cheek into the box with slack marking, allowed himself to be turned easily by the Palace man but was initially relieved to see Pickford push the resulting shot away.
Unfortunately, the goalkeeper only pushed it straight to McArthur who couldn't miss from close range.
A nightmare start was wiped out, however, by some generous refereeing from Anthony Taylor who pointed to the spot when Niasse went down as he tried to charge past Dann towards goal. Leighton Baines stepped up and despatched the penalty with his restored aplomb to level the score with five minutes gone.
Niasse came close to putting Everton ahead 12 minutes later when his determination took him past two defenders but Speroni denied him with an out-stretched palm while McArthur forced a low save from Pickford in the 33rd minute with a placed effort as Roy Hodgson's men continued to dominate the contest.
Two minutes later it was 2-1. Joel Ward was afforded space down the Palace right to whip a cross behind the visitors' defence and in front of Pickford and when Zaha arrived untracked at the back post, he was able to convert a simple chance.
Ademola Lookman lashed a half-volley over the bar but Everton generally lacked penetration and composure and were heading into the interval a goal down when Speroni eschewed the easy option of a long clearance and set up Everton for their second goal.
Dann collected his pass with three grey shirts around him whereupon Gueye dispossessed him and Sigurdsson slipped a pass to the open Niasse. The Senegalese striker kept his cool to slide the ball past the stranded ‘keeper to send the two sides into the break at 2-2.
Unsworth introduced Calvert-Lewin and Davies for Lookman and Schneiderlin at half-time and it resulted in a lot more bite in the middle of the park and some aerial threat up top.
The best chance for the Blues in the second half arrived early and at Calvert-Lewin's feet, however, after Sigurdsson picked him out from the by-line but his left-foot shot was blocked by Speroni.
Sandro Ramirez would come on later for Aaron Lennon but even with three strikers on the pitch, Everton struggled to pose any threat. Thankfully, Palace weren't much better, even after Christian Benteke was introduced for the last quarter of an hour or so.
The Belgian did squander the best chance for Hodgson's side, though, following another error by Keane. Zaha capitalised as the centre-half dithered and knocked it on to Benteke but he dragged a horrible effort wide without troubling Pickford.
Sandro put a later header over the bar from Jonjoe Kenny's cross and Benteke drew a final save from Pickford with a thumping effort in the last minute but the spoils were eventually shared on a sodden afternoon in south London.
David Unsworth dropped Davies and Rooney to the bench for today's vital game at Crystal Palace.
Gueye and Schneiderlin are reunited as the defensive blockers in midfield, while Williams continues to kick his heels on the bench. There is no place for Beni Baningimie in the squad.
Everton fell behind in farcically in the first minute. Straight from kick off the hosts attack as Ruben Loftus-Cheek's shot is parried by Jordan Pickford straight to James McArthur, who taps in from close range.
In a nothing challenge at the other end, Niasse runs into Dann, falls over, and wins a penalty! And Baines slams it home from the spot!!! What a crazy start to such a crucial game.
Nasse got a chance to walk the ball in on Speroni but could not produce a finish. Keane did well to pick out Lennon wide right who beat his man and whipped in a good cross but it was cleared.
It was pretty much rubbish football to watch at times: stupid fouls, poor ball control, no structure, no fluidity, no joined-up football.Everton gave up a couple of corners, Townsend's overhit orner poorly summing up the absolute lack of quality.
Palace were seeing more of the play but a turnover saw Niasse advancing clumsily down the left until he felt a tap on his ankle and fell over again, this time earning a yellow card for Milivojevic. But nothing came from Sigurdsson's free-kick.
McArthur was given another chance to score but Pickford had his shot well covered. Lookman was keen to get involved but could only foul his man. That saw Crystal Palace simply waltz through the non-existent Everton defence, a simple tap-in for Zaha after a sharp cross from Ward on the right, Baines nowhere to be seen.
Niasse finally went in the book for faking it when he jumped up with and fell again far too easily. Palace almost walked it in again as Everton rocked back, looking devoid of any ability to take a grip on proceedings that were rapidly going pear-shaped.
Everton won a corner when Dann headed behind needlessly. It was delivered well enough by Sigurdsson and Lookman fired in nicely on the turn but it was always rising beyond the goal. Keane was booked when Loftus-Cheek turned him well, Cabaye thankfully wasting the free-kick.
Another moment of craziness gifted Niasse a goal, Speroni giving Dann a hospital ball with Gueye in quickly to dispossess him and Sigurdsson poncing on the pass, playing in Niasse who took the chance very well, making him Everton's top scorer with SIX! Farcical football in all quarters of the field.
Unsworth made two changes in response to what he was seeing, Calvert-Lewin replacing Lookman, who had struggled, and Davies replacing Schneiderlin, who again had done nothing. But his charges still strugled with the home side outplaying them again at times.
Niasse fouled Cabaye very poorly from behind... (second) yellow card all day long, but Taylor remarkably let him off. Kenny was also looked upon kindly after a couple of crude fouls in quick succession. Palace continuing to present problems, getting forward and winning corners with Everton penned back.
Calvert-Lewin pressured Sakho, wining the ball, getting fouled, earning the Crystal Palace player a yellow card, and winning a dangerous free-kick for Sigurdsson, but nothing came of it.
At the other end, aggressive play by Davies earned him a yellow card and gave Palace a similar opportunity, blocked by the Everton wall. Meanwhile, Everton won some more corners, but could not fashion a direct chance on goal.
Palace were working harder to create openings and it required some stern defending from Everton to contain them with the minutes ticking away. Everton's counters were spirited but lacking in guile and easily thwarted. Sandro replaced Lennon for the final 15 mins.
Benteke came on and was set up well to strike but fumbled his shot wide. Kenny put in a brilliant cross in the last minute of normal time but Sandro got underneath it, At the other end, Benteke fired straight at Pickford, who punched it away.
Crystal Palace: Speroni, Ward, Dann, Sakho, Schlupp, Loftus-Cheek, Cabaye, Milivojevic [Y:32'], McArthur (75' Benteke), Townsend, Zaha.
Subs: Tomkins, Hennessey, Souare, Fosu-Mensah, Sako, Puncheon.
Everton: Pickford, Kenny, Keane [Y:45'], Jagielka, Baines, Schneiderlin (46' Davies [Y:65']), Gueye, Lennon (76' Sandro), Sigurdsson, Lookman (46' Calvert-Lewin), Niasse [Y:36'].
Subs not Used: Robles, Williams, Rooney, Martina.
Referee: Anthony Taylor
David Unsworth continues at the helm in what, officially at least, remains an interim capacity as Everton resume Premier League action this weekend against Crystal Palace.
The Blues travel to Selhurst Park, the scene of their last away win way back in January, hoping to record back-to-back victories for the first time since September. The successive triumphs over Sunderland in the Carabao Cup and Bournemouth in the League also marked the last time Everton had won in any competition prior to the meeting with Watford last time out.
Now, with the last international break of the year out the way, they are looking to put a run of results together that will get the club back on an even keel and banish further talk of a relegation battle this season.
Having overseen three successive defeats away from Goodison Park since taking over from Ronald Koeman but with the benefit of a further fortnight to get more settled into his role, this promises to be another test of Unsworth's suitability for a longer stint as stand-in manager or as a candidate for the job on a permanent basis.
With seemingly little progress made regarding other options, Unsworth could get a few more games to prove himself and he will know that wins are the only currency that will purchase him a position he clearly covets.
Once again, all eyes will be on his chosen formation, line-up and approach to taking on a team that sit bottom of the division after the worst possible start but one which has shown signs of improvement recently under Roy Hodgson.
The Eagles beat Chelsea 2-1 at home a month ago and drew 2-2 with fellow strugglers West Ham, managing goals for the first time at Selhurst Park while losing only narrowly away at Newcastle and Tottenham.
Hodgson also looks set to welcome Christian Benteke back to his side following injury, one player Everton would have preferred not to be facing given their defensive vulnerabilities this season, particularly at set-pieces.
Unsworth, meanwhile, insists that there are no problems with either Morgan Schneiderlin or Kevin Mirallas following reports and rumours of a lack of commitment and discipline from the duo and that both are available for selection.
Schneiderlin has started only one game in the last month, that his ill-fated appearance at Lyon where he was sent off in the 3-0 defeat while Mirallas hasn't figured since coming off at half-time at Leicester and it would not be a surprise if neither player made the starting XI this weekend.
A starting midfield trio of Idrissa Gueye, Beni Baningime and Tom Davies is more likely again, with Ademola Lookman perhaps providing the width if Unsworth doesn't opt for two strikers.
Depending on how results shake out elsewhere, Everton could rise to 12th with a win, close the gap further on the top half of the table and put more daylight between themselves and the bottom three.
Kick-off: 3pm, Saturday 18 November, 2017
Referee: Anthony Taylor
Last Time: Crystal Palace 0 - 1 Everton
Predicted Line-up: Pickford, Kenny, Keane, Jagielka, Baines, Gueye, Baningime, Davies, Lookman, Rooney, Niasse