The Gunners - outplayed by Barcelona for large spells at home on Tuesday night - made seven changes to their starting XI as manager Arsene Wenger clearly had one eye on next week's Champions League quarter-final second leg at the Nou Camp.
However, despite dominating the home side could not find a breakthrough until deep into five minutes of stoppage time.
Wolves defended bravely and overcame the sending off of captain Karl Henry for a late challenge on Tomas Rosicky only to be denied when Bendtner headed in what could prove to be the young Dane's most vital strike yet.
Bendtner also netted a last-gasp strike as the Gunners defeated Hull last month.
The victory keeps Arsenal on the coat tails of Chelsea and Manchester United with five games remaining.
After Chelsea went back to the top of the table with their controversial 2-1 victory over Manchester United at Old Trafford, Wenger knew there was little margin for error if Arsenal wanted to keep pace as the title race heats up.
Theo Walcott - recalled to the team after his goal against Barcelona - weaved his way into the Wolves box after cutting in from the right, before chipping the ball back across goal where Eduardo forced goalkeeper Marcus Hahnemann into a fine, one-handed reaction save.
Wolves defender Michael Mancienne charged forwards and let fly from 25 yards, which was just off target.
Arsenal went close again when Rosicky pulled the ball back through a crowded six-yard box to find Eduardo, but the Croatian could only stab the ball wide as he lost balance.
Walcott then released right-back Bacary Sagna on the overlap into the Wolves penalty area, and his shot was blocked by Hahnemann.
After 15 minutes, the French defender was in again, this time sliding to hook the ball to Emmanuel Eboue, whose attempted backheel hit his trailing leg.
Arsenal continued to press, with Walcott testing Hahnemann with a 20-yard snap-shot after the ball dropped to him from a corner.
Although it continued to be one-way traffic, Wolves remained solid.
Rosicky created some space for himself on the edge of the area, but could only fire his shot high into the stands, while Denilson then drilled a low effort wide and Mikael Silvestre tested the Wolves goalkeeper again.
Arsenal maintained the pressure at the start of the second half as Silvestre flashed a low centre across goal.
Alex Song collected the ball 30 yards out and charged forwards, only to blaze his shot wide.
Walcott continued to be Arsenal's main attacking outlet, but the home side lacked any real presence in the Wolves box.
Eduardo volleyed wide after reacting quickly to a high ball.
As the hour mark approached, Rosicky cut in from the right and fired a low, angled drive goalwards, which Hahnemann was again behind.
There was still a threat from Wolves, though, as winger Matthew Jarvis flashed a couple of dangerous balls into the Arsenal six-yard box.
After 66 minutes, Wolves captain Henry was shown a straight red by referee Andre Marriner for needlessly going through the back of Rosicky, who was facing his own goal in the centre-circle.
The Czech midfielder needed treatment to his calf, but was soon back on the pitch and forced Hahnemann into another good reaction save before Bendtner stretched the American with a looping header.
Rosicky cleared off the line as Sol Campbell deflected the ball towards his own goal following a Wolves corner.
Arsenal sent on Mexican Carlos Vela to try to find a way through.
Walcott stabbed a close-range effort wide during five minutes of stoppage time.
Then, just when it seemed all over, Sagna whipped the ball into the six-yard box where Bendtner arrived to bullet a header past Hahnemann as the Emirates Stadium erupted.