Arsenal book knockout spot
Second-half goals from Jack Wilshere - his first in almost two years - and Lukas Podolski made sure of at least second place in Group B after leaders Schalke beat Olympiakos.
The Gunners must now win in Athens in a fortnight to stand any chance of finishing top and so head into the last 16 as one of the seeds.
Despite coach Rene Girard accepting their European hopes were all but over in his pre-match press conference, it was a positive start by the French visitors - who were caught up in north London traffic and arrived only an hour ahead of kick-off.
It was Arsenal, though, who fashioned the first opening on ten minutes as they looked to build on their 5-2 Premier League win over north London rivals Tottenham Hotspur on Saturday.
Montpellier failed to clear a corner and the ball was worked out to Wilshere on the left wing, with his cross into the penalty area sent crashing against the bar by a bullet header from Laurent Koscielny.
Arsenal, however, also had to be on their guard from the quick counter-attack as Anthony Mounier got clear behind the defence and goalkeeper Wojciech Szczesny, just back in the side after an injury lay-off, had to come out to the edge of the box to make an important block.
There remained little to chose between the two side as the half-hour passed, Arsenal seeming content to have plenty of the ball if without penetrating the visitors' rearguard.
Podolski looked to fashion an opening himself when moving across the edge of the Montpellier penalty area, but then dragged his low, right-footed shot back wide of the far post.
The German was again off target when played in by Santi Cazorla down the left side, drilling a first-time effort into the side-netting.
Montpellier fired a warning shot as half-time approached when Younes Belhanda broke clear and drilled a 20-yard effort just over the bar. Arsenal took the lead four minutes into the second half.
Captain Thomas Vermaelen floated a deep ball into the penalty area, which was knocked down by former Montpellier striker Olivier Giroud into the path of Wilshere, who lifted the ball over the 'keeper for his first goal since November 2010.
Podolski secures three points
The goal settled Arsenal down, and they were soon on the offensive again with play flowing through Cazorla. It was 2-0 on 63 minutes after another swift counter by the hosts.
Alex Oxlade-Chamberlain carried the ball down the right, before feeding Giroud on the edge of the penalty area. The Frenchman exchanged a neat one-two with Podolski, who ran on to fire a sublime left-footed volley over Geoffrey Jourdren
Arsenal were rampant now, as Montpellier full-back Mathieu Deplagne deflected another Podolski bullet behind. England winger Chamberlain, who looked to have aggravated a hip injury in the build-up to the goal, was replaced on 69 minutes by Wales midfielder Aaron Ramsey.
Montpellier 'keeper Jourdren palmed a floated effort from Cazorla over the crossbar as Arsenal looked to extend their advantage.
Giroud was then denied by his former team-mate, who pulled off a point-blank save with his legs after the Arsenal striker was put into the right side of the penalty area.
Gervinho, out for several weeks with an ankle injury, came on for Giroud while Francis Coquelin replaced Cazorla for the final six minutes.
The hard work, though, had been done as Arsenal moved into the last 16 and will now target victory in Athens next month to keep alive hopes of securing a place among Europe's top seeds for the knockout stages.