A series of fine saves by visiting keeper Marcus Hahnemann and some resolute defending was almost enough to earn Mick McCarthy's side a share of the points.
Arsenal 1-0 Wolverhampton Wanderers: As it happened
But substitute Bendtner met Bacary Sagna's cross from the right to head past the American keeper to send the Emirates faithful into raptures.
The Gunners began quite brightly despite their midweek exertions against Barcelona.
They should have been 2-0 ahead in the first 15 minutes. First Eduardo had time to pick his spot in front of goal but instead scuffed a hurried shot wide of the left post.
Then a minute later, Sagna was released by an inspired Theo Walcott but his powerfully shot was saved by the legs of Hahnemann.
The Wolves keeper showed his bravery a minute later when sliding in to deny Sagna. The ball spilled to Emmanuel Eboue, who instead of turning and shooting went for the elaborate back-heel and the chance slipped away.
Wolves never threatened Arsenal's goal but were more concerned with disrupting the play of the hosts.
Arsenal made a hesitant start to the second half and the Wolves goal was rarely threatened.
Eduardo had an excellent chance in the 54th minute but slipped as he shot and the ball went wide when the keeper should have really been tested.
Tomas Rosicky drew a save out of Hahnemann just before the hour but his low drive from the right was comfortably claimed at the near post.
This was a tired and disjointed performance from Arsenal and, as every minute went by, Arsene Wenger's frustration grew as did Wolves' desire to go forward.
Wolves were reduced to ten men in the 67th minute when Karl Henry was sent off for a savage tackle from behind on Rosicky.
The Czech player dusted himself down and then forced an excellent save out of the Wolves keeper when he latched on to a mis-hit pass from Walcott to shoot from close range.
At the other end, Wolves were awarded a questionable free-kick and the resultant header by Ronald Zubar was cleared off the line by Rosicky.
The Gunners virtually set up camp on the edge of the Wolves area but could not find a breakthrough.
But as the last of the five minutes of injury time ticked away, the ball found its way to Sagna on the right flank.
The full-back sent over a perfect cross for Bendtner to out-muscle his marker and guide a header into the right corner beyond Hahnemann to keep the Gunners in the title race.