Wolves 2 - 2 Everton
Richarlison scored a brace on his debut, the second a superb effort that looked for a while it might earn victory for 10-man Everton
Richarlison scored a memorable brace on his Blues debut but Everton's hopes of getting off to a winning start were undermined by a hugely controversial 40th-minute red card for Phil Jagielka.
The Brazilian put Marco Silva's men in front with a goal in each half but Wolves grabbed a point when their influential young midfielder Ruben Neves added to his first-half goal with an assist for Raul Jimenez to head home 10 minutes from time.
With Richarlison the only one of the six summer signings to make the starting XI, Everton looked fairly comfortable in the early going and after a couple of early corner opportunities went begging, Seamus Coleman had the first shot on target with a fairly tame effort that was easily saved with 10 minutes gone.
Referee Craig Pawson, who would move centre stage later in the first period, was letting a number of testy challenges go from both teams but he was within his rights to book Richarlison with only a quarter of an hour gone for hacking Joao Moutinho down.
The 21-year-old responded, however, by scoring the opening goal three minutes later. Rising between two defenders, Michael Keane got enough on the dead-ball delivery from the left to cause it to drop in front of Richarlison and with his first shot on goal in a Blue jersey, he stabbed the loose ball home from close range.
Moutinho had the first serious shot from the home side when he hammered a rising half-volley over the crossbar midway through the half before Richarlison spurned a chance to play Theo Walcott in on goal with a weak touch off the outside of his boot with the Wolves defence scrambling in retreat.
Everton had half-time in sight when Jagielka put himself in trouble with a loose touch 10 yards outside his area and was caught turning into Diogo Jota's high press. His lunging tackle appeared to make contact with the ball before catching his opponent's heel and sending Jota crashing to the turf.
Pawson flashed the Blues' skipper a straight red card, Neves surreptitiously moved the ball forward five yards into the perfect location for a direct free kick and duly curled the set-piece into the top corner off Jordan Pickford's fingertips.
With Gylfi Sigurdsson sacrificed to bring on Mason Holgate to plug the hole in central defence, Everton not only weathered the first quarter of an hour of the second half but when Cenk Tosun selfishly went for goal rather than slipping the ball through to the wide open Walcott, Rui Patricio was on hand to push the Turk's shot behind.
At the other end, Pickford made a fabulous blocking save to deny Jimenez and the stage was set for a virtuoso second goal from Richarlison. Collecting a lay-off by Tosun, he advanced into the Wolves box and picked his spot with a lovely finish that he bent around the dive of Patricio and inside the fat post.
With a man's advantage, however, Wolves were able to mount sustained pressure for the next 13 minutes and found a way past Pickford again when, after a number of crosses had been repelled, Neves was able to curl the ball over Michael Keane's jump and onto the head of Jimenez who despatched his header inside the post.
Yet Everton might still have won the game had they not wasted a couple of inviting chances on the break, the better of which arrived when substitute Oumar Niasse fed Coleman on the overlap with just one defender back but the Irishman's return pass seeking the Senegalese striker in the middle was wasted.
Silva was, unsurprisingly, angry at the decision that had compromised his team's chances of going on to win this opening match of his tenure but he could take solace from his side's performance in claiming a valuable point.
He will have noted the character in his squad while also taking great satisfaction from the debut performance of his most expensive summer acquisition who already looks like a potential match-winner.