Chamakh struck after only 39 seconds when he headed in a cross from Alex Song and wrapped up victory in injury-time.
It was the perfect riposte after their shock home reversal against Newcastle and kept Mick McCarthy’s side in the bottom three.
The Gunners threatened to run away with the game in the early stages with their one touch football.
Wolves were indebted to keeper Marcus Hahnemann for keeping them in the hunt during that period.
But they hauled themselves back into contention via the creativity of Nenad Milijas and the endeavour of Stephen Hunt.
Arsenal got off to the perfect start through Chamakh’s seventh goal of the campaign.
Song made a break down the right before delivering a probing cross – and Chamakh was first to react in sending his header past Marcus Hahnemann into the corner of the net.
It needed a fine save from Hahnemann to prevent Arsenal from doubling their lead.
Andrey Arshavin raced clear of the Wolves rearguard but Hahnemann came quickly off his line to reduce the angle and he blocked the resulting shot.
The home side were forced to make a change after only eight minutes when Dave Edwards limped out of the action to be replaced by Hunt.
Wolves were taking time to recover from their early setback and were indebted to Hahnemann for a second time.
Arshavin’s low cross was only half cleared by Richard Stearman and Fabregas’ shot was blocked by the feet of Hahnemann.
Wolves were being pulled apart and Christophe Berra had to make a timely block on Arshavin’s shot after being found in space by Fabregas.
Wolves started to get a foothold in the game and Kevin Doyle, without a league goal this season, came close to putting them on level terms after 28 minutes.
Hunt floated in an inswinging free-kick from the right flank and Doyle’s back header was only inches too high with Fabianski scrambling across his goal.
Doyle was then found in space by Milijas’ raking long pass but his control let him down as he bore down on goal and Gael Clichy was able to make the interception.
Fabianski had to palm away a cross from Matt Jarvis that took a wicked deflection off Sebastien Squillaci and was about to creep inside the far post.
Wolves came close to emulating Arsenal’s quickfire start to the first half in the opening minute of the second period.
Jarvis’ low ball across the six yard box was met by Milijas but Sagna made a crucial block to deny him the equaliser.
Arsenal should have doubled their lead after a misplaced pass from Stearman fell to Rosicky outside the Wolves box.
He delivered the ball back into the penalty area to the unmarked Fabregas but he sent his shot wide.
Wolves started to apply pressure and Fabianski tipped over a curling effort from Doyle which looked destined for the top corner of the net.
Rosicky came to Arsenal’s rescue after 58 minutes when he cleared Stearman’s close range effort off the line from Milijas corner.
Wolves were saved by the woodwork six minutes later as Arshavin’s low drive beat the dive of Hahnemann but rebounded to safety off a post.
Arsenal substitute Denilson was booked after 73 minutes for not retreating after Wolves had been awarded a free-kick.
Wolves skipper Karl Henry deflected a low effort off the line from Johan Djourou after Sebastien Squillaci had initially mis-kicked inside the six yard box.
Stearman was yellow carded in the 86th minute for chopping down Arshavin.
Then Fabregas went into the book 60 seconds later for a touch-line lunge on Stephen Ward who was stretchered off and replaced by Steven Fletcher.
Doyle almost rescued a point for Wolves when his low shot flew inches wide.
But in the dying seconds Chamakh wrapped up the points with a clinical piece of finishing.