Louis Saha hit the woodwork and Leon Osman spurned three good chances as Everton failed to make the most of a number of early opportunities to enhance their European claims at Molineux.
But Wolves were competitive throughout and fully merited a point from a feisty encounter.
Both sides had good openings in the second period with Ronald Zubar going closest for Wolves after a brilliant run into the box.
The result extended Everton's impressive run to just two defeats in 18 games but was a setback to their hopes of snatching a Europa League spot.
Hard fought: Everton's Phil Jagielka battles with Kevin Doyle of Wolves
The Toffees were without the on-song Mikel Arteta after deciding torest him as a precautionary measure to protect a slight groin injury.
His place was taken by Jack Rodwell in the only change made by either side after impressive midweek wins.
Everton had travelled on the back of victory over ChampionsLeague-chasing Manchester City while Wolves eased their relegationfears with an emphatic win at West Ham.
Everton had the better of the first-half chances but Wolves werealways in the contest and gave as good as they got in a full-bloodedsecond period.
Wolves appeared to start enthusiastically with Kevin Foley breakinginto the area on the right but Matt Jarvis side-footed his cross wideand Everton then took control.
Osman had the first of his three good chances in quick succession after five minutes.
Steven Pienaar played a one-two with Saha and then picked out Osmanwith a square ball across goal but the midfielder failed to make firmcontact and Marcus Hahnemann saved.
Another opportunity opened up for Osman after Wolves failed to clear a John Heitinga throw-in but he shot wide.
Eyes on the ball: Wolverhampton Wanderers's Ronald Zubar (left) and Everton's Steven Pienaar battle
Saha also shot tamely at Hahnemann after Pienaar let a Phil Nevillecross run and Osman had a third effort deflected into the goalkeeper'sarms.
Wolves showed some attacking threat with David Jones making adangerous run into the box and Zubar fluffing a header from a Foleycross.
Leighton Baines tried to test Hahnemann from distance after an Osmancross was headed out by Michael Mancienne but the American savedcomfortably.
Everton's top scorer Saha showed brilliant control to chest down along ball from deep and to turn and shoot but his fierce 20-yard driveclipped the crossbar and went over.
Wolves had two chances before the break but Jody Craddock shot well over and Jones curled a free-kick straight at Tim Howard.
Osman picked out Saha with a superb cross early in the second halfafter Heitinga had seized upon a loose ball but Craddock just didenough to prevent the Frenchman directing a header on target.
Baines tried his luck from a free-kick at the edge of the box buthis shot was deflected for a corner off the wall and Tim Cahill headedwide from the resulting cross.
Wolves had an opening when a Foley throw made its way to Jarvis but he fired wildly into the stand.
Wolves appeared to grow frustrated as a number of decisions wentagainst them but Neville complained to the referee about the treatmentsome of the Everton players were receiving from the hosts.
Wolves pieced together a nice move but Foley curled an effort over after being teed up by Jones 18 yards out.
Zubar had an even better chance after combining well with KevinDoyle on the right and cutting inside Heitinga but he blazed over.
Chances continued to be created at either end with Pienaar twicegetting into good positions for Everton but miskicking each time.
Wolves substitute Adlene Guedioura attempted a spectacular overhead kick but missed the target.
Zubar then found himself in good space in the box but was unable tobeat Heitinga and an extraordinary goalmouth scrum ended with Doyleshooting over.
Everton substitute Dan Gosling almost had a chance to snatch victoryfor Everton in the last minute but Hahnemann bravely claimed the ballat his feet.
Cahill then twisted himself to get a shot past Hahnemann but Craddock ensured it went wide.
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