The Gunners were ahead after just eight minutes through Gervinho.
However Wolves, struggling at the other end of the table, rallied and levelled on 38 minutes through Steven Fletcher.
The visitors survived the second-half dismissal of midfielder Nenad Milijas as keeper Wayne Hennessey denied the home side time and again.
After a bright start by Wolves, Arsenal broke quickly to take the lead on eight minutes.
Thomas Rosicky fed Yossi Benayoun, whose pass split the Wolves defence as Gervinho beat the offside trap to race clear.
The Ivory Coast frontman, set to soon be away at the African Nations Cup, waited for keeper Hennessey to commit himself, before cutting back inside and then rolling the ball into the net between the two defenders on the line.
Wolves looked in danger of being overrun, as following their positive start, the visitors were forced to defend deeper and deeper.
Gervinho darted clear again and fed Robin van Persie on the right side of the penalty area, but for once the Dutchman - chasing the record for goals in 2011 - was off target as he skewed the ball well wide of the far post.
Benayoun, on loan from Chelsea, was producing an all-action display and charged down the left - only to stumble over the ball when in the penalty area.
Van Persie continued to look for the opening, his chip headed over by Wolves defender Stephen Ward.
To their credit, Wolves had weathered the storm somewhat, only to then almost hit the self-destruct button when skipper Karl Henry lost the ball to van Persie. He fed Rosicky on the edge of the box who in turn laid a pass off to Mikel Arteta and his angled drive was blocked by Ward.
Van Persie then saw his low strike turned around the post by Hennessey.
Out of nothing, Wolves were level on 38 minutes.
Arsenal failed to clear a corner, which Stephen Hunt lobbed back in. His shot was deflected and Fletcher guided a header into the far corner.
Arsenal immediately went on the offensive, but Wolves were more confident and calmly saw their way through to half-time.
The Gunners upped the tempo after the restart, but failed to find a telling pass in the final third.
In the 57th minute, Laurent Koscielny's cross struck Christophe Berra on the arm, but referee Stuart Attwell was not interested - and instead showed a yellow card to Arsenal defender Thomas Vermaelen for complaining.
Arsenal had a free-kick when Gervinho was bundled over by Karl Henry 22 yards out, just left of centre.
Van Persie clipped the ball towards the top corner, with Hennessey touching it over at full stretch.
Per Mertesacker's close-range header was then scrambled clear by the busy Wolves keeper.
Rosicky swept the ball wide from 20 yards after a persistent run by Koscielny.
With tempers at boiling point, Atwell brandished his red card on 75 minutes after a studs-up sliding challenge by Milijas on Arteta.
Van Persie's shot on the turn was deflected behind as Arsenal laid siege to the Wolves goal, with substitute Andrey Arshavin then clipping the outside of the post.
Hennessey pushed away another goal-bound free-kick from van Persie, before Marouane Chamakh came on for Johan Djourou to give the Gunners another attacker in the closing five minutes.
The Morocco striker clashed heads with van Persie at a corner, which left the Arsenal skipper momentarily out of action.
Vermaelen was denied by an inspired Hennessey before Wolves held out through six minutes of stoppage time.
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