Wilshere had gone 725 days without a goal, since he netted against Aston Villa in November 2010, after being sidelined for 14 months with foot and knee injuries.
But the England international finally got back on the scoresheet with a cool finish early in the second half against the French champions and Lukas Podolski's stunning volley soon after sealed a vital victory at the Emirates Stadium.
With Schalke beating third placed Olympiakos in the night's other Group B fixture, Wilshere and Podolski's heroics put Arsenal into the knockout stages of Europe's elite club competition for the 13th successive season.
Arsene Wenger's side remain second in the group, one point behind Schalke, but crucially they have avoided the prospect of a qualification shoot-out with Olympiakos in their last group fixture in Athens on December 4.
Wilshere ran to embrace Arsenal's physio after scoring and he said: "My fitness will come. I've never been injured before so I can't tell you how long it will take.
"The first half was hard. We were sloppy, we gave ball away and weren't ourselves.
"We needed the early goal in the second half. But we have to step it up. Tonight wasn't good enough."
Montpellier coach Rene Girard added: "We lacked something going forward. We saw that in the second half especially.
"We started to struggle physically in the closing stages. I think this was one game too far in terms of the injuries and the players we have missing."
Wilshere, making his fifth appearance of the season, was Arsenal's driving force and he sent over a teasing cross that Laurent Koscielny headed against the crossbar in the early stages.
Arsenal's often creaky back-four were caught out when Montpellier captain Mapou Yanga-Mbiwa slipped a pass through to Anthony Mounier and it took a brave block from goalkeeper Wojciech Szczesny to snuff out the danger.
Yanga-Mbiwa was less assured on defensive duties, the midfielder allowing Podolski to rob him on the edge of his own penalty area before breathing a sigh of relief as the German dragged his shot just wide.
Podolski missed the target again moments later, this time with a miscued effort from a tight angle after Santi Cazorla's pass unhinged the Montpellier defence.
That summed up a lethargic first half from the Gunners. Montpellier had virtually no chance of reaching the last 16 after taking just one point from their four matches, but they were still able to hold out with ease.
However, Wenger's half-time team-talk seemed to reinvigorate Arsenal and they took charge in emphatic fashion after the break.
The hosts were ahead in the 49th minute when Thomas Vermaelen clipped a cross to the far-post and Olivier Giroud rose highest to nod the ball into the path of Wilshere, who cleverly flicked his shot over advancing goalkeeper Geoffrey Jourdren with the outside of his left foot.
It was a cathartic moment for Wilshere after his injury nightmare and Arsenal, now in far more vibrant mood, killed off Montpellier with a sublime second goal 14 minutes later.
Podolski started and finished the move, prodding a pass to Giroud 20 yards from goal and then continuing his run into the penalty area to meet the former Montpellier's forward's return ball with a brilliant volley that flashed past Jourdren into the roof of the net.
Jourdren kept the score respectable for Montpellier with fine saves to deny Cazorla and Giroud, but Arsenal had done enough to ensure their progress.