The enigmatic Walcott added a second two minutes later, before Yossi Benayoun made it three with a precise finish in the 69th minute to wrap up the points for Arsene Wenger’s in-form side as the visitors went five points clear of Tottenham and Newcastle.
It was another crushing defeat for Wolves, who sink further into the relegation mire, while for Arsenal it was their seventh victory in eight games as the Gunners consolidated third spot.
Beleaguered Wolves boss Terry Connor dropped leading scorer Steven Fletcher and fellow striker Sylvan Ebanks-Blake and reverted to a 4-5-1 formation, while Wenger made three changes for the clash as Johan Djourou was recalled in place of the suspended Laurent Koscielny and Andre Santos and Aaron Ramsey stepped in for Kieran Gibbs and Tomas Rosicky.
Wolves came into the match off the back of sixth successive defeats and six points adrift of safety, and it could hardly have started in worse fashion for the hosts as Bassong brought down the flying Walcott and was immediately shown the red card as he conceded the penalty.
The resulting spot kick was utterly audacious as Van Persie sent Wayne Hennessey diving to his right before dinking the ball, as if in slow motion, down the centre of the goal to put the visitors in front.
The prolific Dutchman has now scored 45 goals in his last 50 Premier League games, while Wolves have now gone 16 games at Molineux without a clean sheet.
Walcott again terrorised the Wolves defence as he flew through with another blistering run, and a one-two with Van Persie left him to unleash a clinical finish to comprehensively beat Hennessey. It was the England winger’s third goal in his last four games.
Wolves did enjoy fleeting forays into the Arsenal half as Berra rose imperiously to meet a corner from the right as he beat Djourou to the high ball, but a deflection off the defender's back took the ball agonisingly wide.
Nenad Milijas – who was given a controversial red card in the reverse fixture at the Emirates Stadium earlier in the season - replaced David Edwards as Connor made his second change just before the hour mark, but the hosts continued to be overrun in midfield.
Van Persie perhaps should have doubled his tally from close range as he stole in to meet a precise cut back from Mikel Arteta, who produced a lung-busting run to the right byline, but the forward drove his low shot wide of the near post.
Wolves were convinced they had grabbed a goal back in the 61st minute as Doyle headed powerfully towards the far corner of the net from a dinked cross by Matt Jarvis, only for Wojciech Szczesny to pull off a quite spectacular save diving back to his right to claw the ball away from his goal.
But Arsenal were the more clinical as Song twisted and turned out on the left flank before finding Benayoun on the edge of the Wolves box, and the midfielder wrong-footed Hennessey with a crisp shot inside the near post to further stretch the visitors’ lead.
Hennessey made a fine save with his legs to deny Benayoun from close range late on, but the home fans were left to exit Molineux in disgruntled fashion once more as Arsenal coasted through the final stages with consummate ease.
The victory sees Arsenal pull five points clear of rivals Tottenham and Newcastle with five games remaining, while Wolves’ sorry plight goes from bad to worse with Connor’s side still six points from safety and having lost their last eight successive games at home.