Everton dominated both in terms of possession and chances but despite having the ball in the net twice and a good penalty shout waved away, Wolves showed fighting spirit to keep the visitors out.
David Moyes's men hit their stride from the outset, piling the pressure on the Wolves defence, with Tim Cahill squandering a glorious chance in the opening minutes as he hit his shot straight at Dorus De Vries.
The chances continued to come thick and fast and Everton should have had a penalty as Leon Osman appeared to have his heels clipped just inside the box but referee Lee Mason waved away the appeals.
Everton again appeared to be robbed of a goal moments later. Pienaar played in Nikica Jelavic who finished neatly past De Vries, only for the linesman's flag to deny the visitors.
Replays suggested he was played onside by two Wolves defenders. But Everton had only themselves to blame on the half hour mark as Marouane Fellaini headed wastefully wide from James McFadden’s cross with the goal at his mercy.
Content to defend deep and play on the break, Wolves’ chances were few and far between, Stephen Hunt and Steven Fletcher content to shoot from distance.
A similar pattern emerged in the second half, Jelavic again going close with a free kick that De Vries turned behind. And the Croat really should have made it nine goals in 11 league appearances for Everton when he latched onto a Fellaini header to close in on goal, only to drag his shot wide with just the keeper to beat.
The visitors had the ball in the net for a second time only a minute later through Denis Stracqualursi, on for McFadden, but Fellaini was correctly ruled offside from Pienaar's cross.
It was as close as Everton would come to breaking the deadlock and the post match stats said it all: 10 shots on target to Wolves’ one as Tim Howard enjoyed one of his quieter days at the office.