Younes Belhanda stunned the visitors with a ninth-minute Panenka penalty but Arsenal hit back through quick-fire goals from Lukas Podolski and Gervinho to secure only their sixth win in their last 16 group-phase away games.
Remy Cabella hit the bar for Montpellier, who gave Arsenal several uneasy moments, and despite the result, the hosts' display belied a difficult start to their Ligue 1 title defence that has seen them beaten three times already.
Arsenal, meanwhile, have now recorded three straight wins after Premier League successes over Liverpool and Southampton, although Olivier Giroud is still without a goal after failing to score on his return to his former club.
Montpellier coach Rene Girard had called on the club's fans to make Stade de la Mosson "hell" for the visitors but there was a nervousness in the hosts' ranks until Belhanda's penalty brought the stadium roaring to life.
The penalty award appeared harsh but replays vindicated referee Carlos Velasco Carballo's decision to penalise Thomas Vermaelen for a robust challenge on Belhanda, who beat Vito Mannone with a nonchalant chipped spot-kick.
It was a better start than Montpellier's fans could have hoped for on their team's first ever appearance in the competition, but within only nine minutes the French champions found themselves behind.
Giroud had received a warm reception from the supporters of his former club but he created the equaliser in the 16th minute with a prodded through ball for fellow summer signing Podolski that the German guided past Geoffrey Jourdren.
Montpellier barely had time to gather their senses before Arsenal struck again, as Gervinho ghosted into the six-yard area to convert Carl Jenkinson's low cross from the right.
In response, Cabella drew a save from Mannone with a low drive, while Giroud threatened to open his Arsenal account just before half-time with a volley from a Kieran Gibbs cross that flew wide.
Montpellier began to pin Arsenal back in the second period, with a succession of chances early in the half serving to raise the volume in the stadium.
Garry Bocaly and Anthony Mounier both shot off-target, while Cabella fired over after dispossessing the dallying Abou Diaby and then saw a carefully weighted chip from 20 yards come back off the bar.
Back in the Arsenal team after injury, Diaby looked ponderous at times, but in the 57th minute he drove forward and released Santi Cazorla for a shot that Jourdren had to beat away.
Belhanda's promptings were at the heart of much of Montpellier's best football, but he spurned a glorious chance to bring his side level in the 80th minute.
After tip-toeing around the prone Per Mertesacker, the Moroccan playmaker found himself with a clear sight of goal, but from 10 yards out he could only shoot straight at Mannone.
Source: AFP
Source: AFP