And it was Everton who almost took a surprise first-minute lead when Saha picked up Donovan's cross from the left side of the area but screwed a left-footer agonisingly the wrong side of the post.
Tottenham recovered their composure in short order, though, and a loose pass by Donovan let Emanuel Adebayor in for the home side's first chance of the evening but, thankfully, the big striker blazed wide under pressure from John Heitinga.
Five minutes later, another slack pass in the centre by Bilyaletdinov gifted the ball to Spurs but Gareth Bale's cross deflected behind off Neville before Everton could be punished for their profligacy.
Under constant pressing of the ball by Spurs, David Moyes's side struggled to play their way through midfield despite a clearly deliberate attempt to slow the game down and pick their passes.
Too often, though, Tottenham were quicker to the ball and speedier in thought as evidenced when Bale raced forward on the counter and slipped the ball invitingly inside to Adebayor in front of Howard but the on-rushing 'keeper prompted the striker to take too heavy as touch as he tried to round the American and it rolled out for a goal kick.
A goalmouth melee five minutes later after Luca Modric had a decent shout for a penalty waved away by referee Martin Atkinson then gave Adebayor another great chance to break the deadlock but he poked wide of goal from eight yards out.
Back-to-back chances for Everton 13 minutes from half-time suggested that they might still spring a surprise if they could get things together in attack but Saha dragged one shot wide with Anichebe in close support and Donovan drifted a left footer well over from outside the box.
Three minutes later, after Rafael van der Vaart had curled a dangerous shot onto the roof of the net, Spurs went ahead. a long diagonal ball by Younas Kaboul aimed for Aaron Lennon should have been easily dealt with by Baines but he mis-controlled and was dispossessed by the winger, who cut into the area and scuffed a low shot past Howard who was preparing to dive the other way and it was 1-0.
Bilyaletdinov had a difficult chance to level matters going into the interval when the 'keeper could only punch Baines' free kick to him on the edge of the area but the Russian half-volleyed high and wide of goal.
Everton fared little better in the second half as Tottenham remained comfortable in defence and in their superior possession.
Bale went on another of his 50-yard charges towards the Blues penalty area five minutes after the break but Howard was able to paw his deflected shot to safety.
At the other end, Saha's attempt to turn Baines' low cross inside the near post deflected off Matthew Dawson for a corner while Fellaini should probably have done better four minutes later when could only steer Donovan's center high over the bar.
Either side of the hour mark, further disaster struck Everton: first, Distin, having picked up another injury, was forced to walk gingerly from the field to be replaced by Shane Duffy; then, with Cahill backing off in front of the Everton defense, Assou-Ekotto lined up a drive from 35 yards that he arrowed perfectly into the far corner beyond Howard's despairing dive to double Spurs' lead.
That was pretty much it. The Blues visibly faded after that and were it not for Royston Drenthe, who replaced the wholly disappointing Anichebe after 68 minutes, they might not have troubled the Tottenham defence much further.
The Dutchman was his usual effervescent self, though, and when he went down twice in quick succession under clumsy defensive challenges without referee Atkinson batting an eyelid, you knew there was going to be no grandstand finish.
The second foul was clearly a penalty as Kaboul visibly caught Drenthe's heels as he tried to out-pace him to the byline. Had it been awarded, Everton might not only have tested Brad Friedel for the first and only time in the entire game but they could also have set up an exciting last 10 minutes or so.
As it was there was little to cheer for the traveling Blues, not even when great work by Drenthe down the left set up a nice chance for Saha but he sliced his shot awfully and it sailed into the stands.
And that pretty much summed things up...
Injuries or no injuries, this is a poor team playing desperately poor football and precious little ability to score goals regularly, particularly from open play. Despite their best efforts to keep the ball this evening, as soon as they were pressured it invariably ended with a ball forward — Anichebe and Saha hardly won anything in the air —or a horribly mis-placed pass.
From Donovan to Fellaini to Cahill, Neville and Bilyaletdinov, so many were guilty of being casual or sloppy with the ball and on a couple of occasions it might have cost the Blues more dearly.
Moyes will point at the injury crisis and others the lack of investment and both are clearly factors but this entire season, irrespective of the personnel, has been dominated by the salient impression of a team that just isn't functioning how it should.
Player Ratings: Howard 6, Neville 5, Distin 7 (Duffy 7) Heitinga 6, Baines 6, Fellaini 6, Cahill 5, Bilyaletdinov 5 (Gueye -), Donovan 6, Anichebe 5 (Drenthe 7), Saha 6
The fixtures have been coming thick and fast for Everton since Christmas and with that increased congestion in the calendar has come a glut of injuries that again has David Moyes down to the bare bones of what is already an uncomfortably small squad.
Hardly ideal circumstances in which to visit Tottenham Hotspur who are on the kind of run that they haven't enjoyed in the top flight for 50 years — indeed victory for them would draw them level on points with Manchester United in second place in the Premier League. Spurs have won 13 of their 19 League games so far and are certainly in the kind of groove that makes this a daunting prospect for an Everton side that is struggling for form, confidence and, most importantly, goals.
Phil Jagielka heads the list of those players who are either certainly or potentially ruled out of the trip to White Hart Lane. The defender is out until the end of February at least and he is joined on the sidelines by Leon Osman (knee), Ross Barkley (knee), Jack Rodwell (hamstring), Tim Cahill (groin) and Tony Hibbert (groin), with Seamus Coleman, who suffered a recurrence of his thigh strain against Tamworth on Saturday, also highly doubtful.
That would leave Moyes with few options, particularly in a defence shorn of Hibbert and Coleman. Phil Neville — he'll be matched up again with Gareth Bale — and Leighton Baines would be obvious choices at full-back while Sylvain Distin and John Heitinga are the likely candidates to continue in the centre. Shane Duffy is an option, however, that would allow the Dutchman to fill a gaping hole in central midfield.
Marouane Fellaini is, thankfully, fit again but with Diniyar Bilyaletdinov and James McFadden so disappointing in the cup at the weekend, there are no obvious candidates to partner him unless Heitinga does move forward again. Landon Donovan is in line for this third appearance since returning on loan from LA Galaxy, while Royston Drenthe could be deployed on the left flank in what might a more attacking line-up than the manager would be comfortable with,
Up front, with Cahill out it's probable that Moyes will perm two from Louis Saha, Victor Anichebe and Denis Stracqualursi, with Apostolos Vellios seemingly frozen out of contention despite netting three goals so far this campaign.
It has been Moyes's wont to try and contain the better sides on their own ground and hope to grab something from a set-piece. That strategy may get punished by Spurs in the same way that the Blues were undone by Manchester City at the Etihad Stadium. Three points would provide a massive shot in the arm and, with the old adage of "it's 11 v 11 on the day" in mind, it's by no means impossible but, under the circumstances, a point from this rearranged fixture would be an excellent result.
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