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.
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."