But they struggled to find a rhythm in the first half, the closest they came was when Laurent Koscielny crashed a header against the bar.
However, the breakthrough came in the 50th minute when Thomas Vermaelen's cross was flicked on by Giroud and Wilshere pounced on the lay-off.
Wilshere skilfully and subtly lifted the ball over Montpellier keeper Geoffrey Jourden with the sort of clever finesse that both Arsenal and England have missed in his injury absence.
Wilshere loved the moment, celebrating wildly and that gave Arsenal a new momentum even if Montpellier continued to fight hard until the home side's second goal finally broke them in the 63rd minute.
Once again, Giroud provided the assist - his sixth of the season - as the ex-Montpellier striker swapped passes with Podolski and the German forward then lashed a left footed volley into the roof of the net.
With Schalke also winning at home to Olympiacos, the win was enough to take Arsenal through even though Wilshere insisted they must improve to progress even further.
Wilshere added: "We need to finish top. We have to step it up. Tonight wasn't good enough, especially in the first half. We've got to play the best teams to win it so it doesn't matter who we get."
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