Wolves avoided equalling a Premier League record of 10 straight home defeats with a scrappy draw.
Everton controlled the opening period, with Nikica Jelavic having an effort controversially ruled out for offside and Steven Pienaar also threatening.
The hosts improved after the interval but Everton still looked more dangerous with Jelavic dragging wide with their best opportunity.
But relegated Wolves earned a first home point since 4 December.
Did you know?
Everton's James McFadden made just his fifth Premier League start since May 2010.
A fortnight after their demotion was confirmed with a 2-0 home defeat by Manchester City, Terry Connor's team finished their final home game with the kind of defiance that has been absent for most of the season.
With Connor facing an uncertain future and several key players, including Steven Fletcher and Matt Jarvis sure to attract interest from elsewhere, it will be a significant summer for the club. They finish their campaign with a trip to Wigan next Sunday.
Everton manager David Moyes will be frustrated that his team could not translate their dominance into a victory as they extended their unbeaten run to eight games.
Moyes is also facing a pivotal few weeks and the Scot will meet chairman Bill Kenwright to discuss his future after the Blues finish the campaign at home to Newcastle.
Although they could not find a finish - a surprise given they had scored 13 goals in their previous four league games - it was the only thing missing from yet another impressive Everton performance.
Pienaar underlined why Moyes is so keen to keep him when his loan spell from Tottenham expires and James McFadden, whose contract expires this summer, also added creativity in the wide areas in only his second Premier League start of the season.
Leon Osman felt he should have been awarded a penalty after going down under Michael Kightly's challenge after Jelavic and McFadden went close.
The visitors felt hard done by once again when Pienaar guided a pass through for Jelavic, who produced a neat finish only to be called back for offside despite replays showing the Croatian appeared to be level with Ronald Zubar.
Wolves only really threatened from set-plays, with Stephen Hunt lifting a shot over and Fletcher thumping high and wide.
After the break Fellaini planted a header over from six yards after being picked out by Tony Hibbert's cross at the other end.
Wolves keeper Dorus de Vries was at full stretch to push away Jelavic's well-struck free-kick and, as the game degenerated, David Edwards missed with a header from a cross from Kightly, who scuffed wide shortly afterwards.
Jelavic was wasteful once again when he dragged wide after racing clear on to Fellaini's long header and substitute Denis Stracqualursi had another effort ruled out for offside as both teams had to settle for a point.
Wolves manager Terry Connor:
"Everton have not lost in seven, they've scored four goals in three of their last four games, they're a team bang in form, so to get a clean sheet from our point of view is a good effort.
"It was important to try to leave the fans with something. If we couldn't win it then we wanted to take something from the game so they had something positive to go home with for the summer, and come back next year to support the club in its quest to be back in the Premier League.
"We tried to stay with the game, not concede goals, and nick something if we could."
Everton assistant manager Steve Round:
"The players are disappointed in the dressing room. We had enough dominance in possession and created enough opportunities definitely.
"We just couldn't take that defining moment, whether it was the pass or the final shot, and obviously we had a really good goal disallowed.
"I thought the second one was offside, Fellaini doesn't touch the ball but he does go for it, which makes him interfering. Recently we've been playing as well as that but taking the chances, and today we didn't."
Live Text Commentary
Full Time The game is over, as the referee blows his whistle.90:00 +2:30
Corner taken by Steven Pienaar from the left by-line, George Elokobi makes a clearance.90:00 +1:17
The referee blows for offside. Direct free kick taken by Dorus De Vries.89:02
Unfair challenge on Kevin Doyle by Johnny Heitinga results in a free kick. Kevin Doyle restarts play with the free kick.88:08
Richard Stearman fouled by Denis Stracqualursi, the ref awards a free kick. Dorus De Vries takes the free kick.82:57
Sylvan Ebanks-Blake is caught offside. Phil Jagielka takes the direct free kick.82:05
Tony Hibbert takes a shot. Blocked by Stephen Ward.81:04
Sylvan Ebanks-Blake produces a right-footed shot from just outside the penalty box that misses to the left of the goal.79:59
Stephen Hunt challenges Magaye Gueye unfairly and gives away a free kick. Phil Jagielka takes the free kick.78:47
Centre by Leon Osman.77:56
Sylvan Ebanks-Blake is caught offside. Phil Jagielka takes the indirect free kick.76:42
Steven Pienaar has an effort at goal from deep inside the area missing to the left of the goal.75:23
Magaye Gueye takes a shot. Blocked by Richard Stearman.75:05
Nikica Jelavic takes a shot. David Edwards gets a block in.74:28
Outswinging corner taken by Magaye Gueye from the left by-line.73:55
The offside flag is raised against Sylvan Ebanks-Blake. Tony Hibbert takes the free kick.72:58
The official flags Denis Stracqualursi offside. Dorus De Vries restarts play with the free kick.72:20
Marouane Fellaini is flagged offside by the assistant referee. Dorus De Vries takes the free kick.71:19
Nikica Jelavic produces a right-footed shot from the edge of the box and misses to the left of the target.70:34 Substitution
Substitution Michael Kightly goes off and Anthony Forde comes on.
Marouane Fellaini has a shot on goal from outside the box which misses right.67:38 Substitution
Substitution Tim Cahill goes off and Magaye Gueye comes on.66:19
Michael Kightly produces a right-footed shot from just outside the penalty box that goes wide left of the target.65:31
Michael Kightly delivers the ball, Header on goal by David Edwards from just inside the area goes over the target.62:34
The official flags Denis Stracqualursi offside. Indirect free kick taken by George Elokobi.62:15
The referee blows for offside. Free kick taken by Stephen Ward.59:57 Substitution
Substitution Steven Fletcher goes off and Sylvan Ebanks-Blake comes on.59:35
Outswinging corner taken from the right by-line by Steven Pienaar.58:58
Denis Stracqualursi takes a shot. Blocked by Stephen Ward. Outswinging corner taken right-footed by Steven Pienaar from the right by-line.57:58 Substitution
Substitution Denis Stracqualursi on for James McFadden.56:52
Free kick awarded for a foul by Karl Henry on Steven Pienaar. Shot on goal comes in from Nikica Jelavic from the free kick, Dorus De Vries makes a save.53:27 Substitution
Substitution Christophe Berra goes off and George Elokobi comes on.52:16
Unfair challenge on Stephen Hunt by James McFadden results in a free kick. Direct free kick taken by David Edwards.51:47
Kevin Doyle takes a shot. Blocked by Phil Jagielka.51:24
Nikica Jelavic is flagged offside by the assistant referee. Indirect free kick taken by Richard Stearman.48:04
The ball is sent over by Tony Hibbert, Header from deep inside the area by Marouane Fellaini goes over the bar.46:24
Foul by Leon Osman on Karl Henry, free kick awarded. Free kick crossed left-footed by Stephen Hunt.45:20
Kevin Doyle fouled by Leon Osman, the ref awards a free kick. Michael Kightly takes the direct free kick.45:01
The second half has started.45:00 +1:17 Half time
Half Time The players leave the pitch at half time.43:40
Unfair challenge on David Edwards by Marouane Fellaini results in a free kick. David Edwards restarts play with the free kick.40:25
Effort on goal by Steven Fletcher from just inside the penalty area goes harmlessly over the target.37:35
Michael Kightly concedes a free kick for a foul on Sylvain Distin. Johnny Heitinga takes the direct free kick.36:18
Stephen Hunt takes a shot from just inside the penalty box which clears the crossbar.35:04
Foul by Marouane Fellaini on Stephen Ward, free kick awarded. Stephen Ward takes the direct free kick.34:42
Leon Osman takes a shot. Save made by Dorus De Vries.33:38
Sylvain Distin crosses the ball, save by Dorus De Vries.31:38
Free kick awarded for an unfair challenge on Ronald Zubar by Marouane Fellaini. Dorus De Vries takes the free kick.30:13
Tony Hibbert sends in a cross, Marouane Fellaini takes a shot. Ronald Zubar gets a block in. Steven Pienaar takes the inswinging corner, clearance by Kevin Doyle.27:23
Nikica Jelavic is flagged offside by the assistant referee. Christophe Berra takes the free kick.26:35
Marouane Fellaini is ruled offside. Karl Henry takes the free kick. Effort on goal by Steven Pienaar from inside the penalty area goes harmlessly over the bar.25:14
Foul by Johnny Heitinga on Kevin Doyle, free kick awarded. Stephen Hunt produces a cross, Christophe Berra has a headed effort from close range and clears the bar.23:54
Steven Pienaar takes a shot. Save by Dorus De Vries.23:33
Unfair challenge on Marouane Fellaini by Christophe Berra results in a free kick. Leon Osman takes the direct free kick.22:54
Corner from the right by-line taken by James McFadden, save by Dorus De Vries.22:29
Tony Hibbert takes a shot. Blocked by Stephen Ward.21:37
Steven Fletcher handles the ball and concedes a free kick. Direct free kick taken by Tim Howard.19:54
Stephen Hunt gives away a free kick for an unfair challenge on Nikica Jelavic. James McFadden produces a strike on goal direct from the free kick.18:44
Corner taken short by Steven Pienaar.17:51
James McFadden produces a right-footed shot from the edge of the area and misses to the left of the target.16:47
Stephen Hunt takes the outswinging corner, Phil Jagielka makes a clearance.16:14
Outswinging corner taken right-footed by Michael Kightly from the right by-line.15:26
Free kick awarded for an unfair challenge on Christophe Berra by Marouane Fellaini. Free kick taken by Dorus De Vries.13:31
Nikica Jelavic takes a shot. Blocked by Richard Stearman.11:25
Phil Jagielka fouled by Kevin Doyle, the ref awards a free kick. Direct free kick taken by Phil Jagielka.9:19
Outswinging corner taken right-footed by Michael Kightly from the right by-line.9:15
The ball is delivered by Stephen Ward, Sylvain Distin manages to make a clearance.8:28
James McFadden is caught offside. Stephen Ward restarts play with the free kick.7:33
The ball is sent over by James McFadden, clearance by Richard Stearman.4:19
Tim Cahill takes a shot. Save made by Dorus De Vries.2:59
Free kick awarded for an unfair challenge on Steven Pienaar by Karl Henry. James McFadden delivers the ball from the free kick left-footed from left channel, clearance made by Stephen Ward.1:17
Kevin Doyle is flagged offside by the assistant referee. Tim Howard restarts play with the free kick.0:00
The referee gets the game underway.
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