Second-half goals for 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 Olympiacos.
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.
It was a positive start by the French visitors, but it was Arsenal who fashioned the first opening on 10 minutes. 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 had to come out to the edge of the box to make an important block.
Podolski looked to fashion an opening himself when moving across the edge of the Montpellier penalty area, but then dragged his shot wide. Montpellier fired a warning shot as half-time approached when Younes Belhanda broke clear and drilled a 20-yard effort just over the bar, but 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.
Arsenal were on the offensive soon enough and 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-foot volley over Geoffrey Jourdren
Arsenal were rampant now, as Montpellier full-back Mathieu Deplagne deflected another Podolski bullet behind. 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. 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.
Source: PA
Source: PA