But Everton will know they should have picked up all three points as they were dominant in terms of possession and chances created but could not find a way to crack a resolute Wolves defence.
Having taken seven points from three successive away games, Wolves were determined not to let that good run end in front of their own fans as they took another giant step closer to ensuring their Premier League status for a second season.
Everton were equally in-form, having gone into the game on the back of three wins from their previous matches.
But some poor finishing, goalkeeper Marcus Hahnemann and the crossbar cost them the chance too record back-to-back away wins for the first time this season.
The tone was set after just five minutes when Steven Pienaar and Louis Saha combined to set up Leon Osman, who saw his close-range shot turned away by Hahnemann.
Osman then fired wide when well placed before Hahnemann saved from Saha.
USA international Hahnemann was by far the busier of the two keepers and he again denied Osman following good work by John Heitinga and Leighton Baines, before the woodwork came to the rescue of Wolves in the 37th minute.
A long ball up field by Sylvain Distin picked out Saha, who had managed to escape the attentions of Christophe Berra.
The former Manchester United striker let fly from 20 yards and beat Hahnemann only to see his shot crash off the top of the bar.
Saha should then really have finally made Everton's pressure pay off in the 53rd minute when he was picked out by a cross from Osman.
The French marksman was only six yards from goal but headed over under pressure from Jody Craddock.
Baines then saw a free-kick deflected wide and Tim Cahill was just off target with a header before Everton's wastefulness in front of goal threatened to come back and haunt them.
Wolves created one real chance of note in the game and that fell to right-back Ronald Zubar in the 75th minute.
Zubar, who had been on target in the midweek win at West Ham, powered into the area after exchanging passes with Kevin Doyle before unleashing a fierce drive that whistled just wide of Tim Howard's far post.
Everton's frustration was then summed up in stoppage time when Dan Gosling was left with just Hahnemann to beat from four yards only to come off second best in his tussle with the former Reading keeper.