London - A 10-man Everton so nearly overcame a spirited Wolves in their opening 2018/19 Premier League clash as Richarlison bagged a brace but the match ended in a 2-2 draw.
Richarlison announced his arrival to the Everton fans with a close-range finish and superbly curled effort, but Ruben Neves scored a sensational free-kick after Phil Jagielka was dismissed and Jimenez claimed a share of the spoils with his late goal.
Everton started brightly with Gylfi Sigurdsson swinging in an early free-kick that was cleared out for a corner.
Jordan Pickford had to be alert to tip a dipping shot from Ruben Neves over his goal.
And after a succession of Everton corners, with Everton on top, they were soon ahead as Richarlison smashed in from close range, on 17 minutes.
A super Leighton Baines free-kick from wide on the left was challenged in the air by Michael Keane and Willy Boly before the ball dropped to the goalscorer.
Everton were buoyed by the goal and were passing the ball around with composure and cutting out any potential Wolves' attacks.
There was little in the way of goalmouth action though with much of the play limited to the midfield, as Everton free-kick from Baines was cleared at the second attempt by Wolves.
Raul Jimenez twisted and turned into the Everton box until he was crowded out by Morgan Schneiderlin.
Wolves were upping their game towards the end of the first half and Phil Jagielka and Idrissa Gueye combined to clear the danger.
Richarlison wasted a great chance to play in Theo Walcott on the break with a soft touch easily cut out before Pickford got down well to save a decent hit from Helder Costa on 39 minutes.
Everton were then dealt a major blow with Jagielka dismissed for a lunge on Diogo Jota with five first-half minutes remaining.
Mason Holgate was introduced for Sigurdsson as Marco Silva looked to shore up his defence.
The Toffees boss was hoping to see out the half but Neves fired in the resultant free-kick from the edge of the area into the very top right-hand corner of the net.
Wolves came out for the second half with some more positive approach play as they looked to make their man advantage count.
Everton were unable to make anything from an early corner while Walcott couldn't control a sprayed ball from Richarlison as the Toffees looked somewhat down and out.
Jimenez was in a good position in the box but Matt Doherty failed to find him with an over hit cross, as a cross from Joto bypassed everyone in the Everton box, and long-range Neves shot dipped over the goal from a long way out.
Cenk Tosun, meanwhile, may have done better at the other end after breaking through his challenge, only to hit his shot at Rui Patricio, who palmed the effort wide.
Keane couldn't direct his header from a corner on the hour mark while Pickford made a terrific block to deny Jimenez seconds later.
Walcott was unlucky not to be able to get his boot to a good Richarlison knockdown so the Brazilian took the game by the scruff off the neck with a cool, low, curled finish past Patricio from the left hand side into the bottom right-corner of the net.
Helder Costa came off for Leo Bonatini for Wolves on 70 minutes as Ruben Vinagre replaced Jonny Castro.
Joao Moutinho was working hard to try and create an equaliser for his side while Jimenez smashed a volley on target only for Keane to block the effort.
Doherty's delivery's from the right kept being swung in, although it was a cross from left from Neves to pick out Jimenez that drew Wolves back into this tie, as he headed home at the back post - for a deserved leveller.
Omar Niasse came on for Tosun on 82 minutes for Everton in a bid to find a third goal, but Seamus Coleman couldn't find the substitute striker with a curled pass that was overhit.
There would be no hat-trick from Richarlison as he went off with a slight knock with five minutes to play, as Lucas Digne replaced the double goal scorer.
Both sides continued to look for a winner but ultimately it was a point apiece for a new-look Everton and newly-promoted Wolves for the first draw of the opening weekend of the new season.