Wilshere's sharp finish shortly after half-time and the growing signs of a partnership developing between Podolski and former Montpellier favourite Olivier Giroud made it a satisfying evening for manager Arsene Wenger who has now led his side into the last 16 for the 13th consecutive season.
Podolski wasted two great chances in a frustrating first half as Arsenal looked to bounce back from a 2-0 defeat by Schalke in their previous home game in the competition, but the hosts turned on the style after the break.
"We needed two good results, our result and the Schalke result, and we got them so we are happy," Wenger told reporters.
"The first half we had problems but in the second half we moved the ball better and scored two good goals.
"Jack had a difficult start in the game but he got stronger and stronger after the goal."
"We will take a full-strength side there," Wenger said of the clash in Athens. "We will play to win the group."
Buoyed up by a morale-boosting 5-2 win over Tottenham Hotspur in Saturday's North London derby, Arsenal began brightly and nearly went ahead after 10 minutes when Laurent Koscielny thumped a powerful header against the crossbar.
It took the home side 20 minutes to threaten again when Montpellier failed to clear a ball in their area and Podolski weaved across the area before sliding a shot just wide of Geoffrey Jourdren's right-hand post.
Podolski went close again a few minutes later when his left-foot effort flew agonisingly wide of the other post after Santi Cazorla's clever pass released him.
