Everton have been coming up on the rails for a European place but their impressive charge stalled at Molineux. David Moyes' team had scored 11 times in their past four games yet the goals dried up here.
The visitors missed the creativity of Mikel Arteta, who sat out the game with a groin strain and was replaced by Jack Rodwell. Moyes admitted it was two points lost. "We created a lot of opportunities but didn't finish them off," he said. "I think the game was such a scrappy affair, I'm not sure Mikel would have had the chance to get the ball down."
Even the lure of drawing level on points with Liverpool – who play Sunderland today – did not seem enough of a carrot for Everton, although they dominated throughout. But Moyes was satisfied after the team's midweek exertions, when they became the first team to win at Manchester City this season, to earn four points from the two games. "That's a decent haul," he said.
His opposite number, Mick McCarthy, was understandably delighted with a point. "I would have taken it before it started," he said. "It could have been none at all."
With the England manager, Fabio Capello, watching, Everton's Leighton Baines and Phil Jagielka put in solid performances. But so did American goalkeepers Tim Howard and Marcus Hahnemann. The former could start against England in their opening World Cup game on 12 June.
Hahnemann saved twice early on from Leon Osman, who also sent another shot wide in the first half. Louis Saha's long-range rocket bounced off the bar in the 37th minute and he again went close in the second half, heading over under pressure from Jody Craddock. Everton continued to build momentum, winning free-kicks but failing to do anything with them. With 10 minutes to go, Steven Pienaar was in a good position but scuffed his volley and Hahnemann saved.
Dan Gosling also had a chance saved late in the game, while Tim Cahill's attempt at a bicycle kick in injury-time was cleared off the line by Craddock.
Wolves also went into this game on a good run and were fresh from a 3-1 win over West Ham on Tuesday. Kevin Foley's shot was easily cleared by Phil Neville, who was making his 500th club appearance, and Ronald Zubar's cross into the box was cleared by a Jagielka header in the first half.
Foley sent a ball over the bar in the second half, as did Zubar, but what Wolves lacked in attack, they made up for in defence to gain another crucial point towards safety.
Referee: Mike Jones
Man of the match: Hahnemann
Match rating: 6/10