Second-half goals from Jack Wilshere (49') and Lukas Podolski (63') sealed victory for Arsene Wenger's side. Olivier Giroud recorded two assists for the Gunners, who advanced out of the group stage of this competition for the 13th straight season.
Here are five lessons we learned from the match.
Arsenal's recent mini-crisis appears to have ended, and for now, the pressure is off the Gunners in the Champions League.
One match remains in Group B, but Arsenal have already qualified for the knockout stage. That means manager Arsene Wenger can approach the group finale at Olympiakos any way he chooses.
Arsenal have been eliminated from the Champions League in the Round of 16 each of the past two years, so Wenger might chase a result in Greece two weeks from now.
Or not. As group winners in the 2010-11 season, Arsenal drew Barcelona in the Round of 16 and lost anyway.
It's just a guess, but Wenger could use the Olympiakos match to rest key players and experiment with his squad.
Arsenal lost early leads twice in recent weeks.
First, the Gunners drew 2-2 at home to Schalke in the Champions League after leading by two goals in the first half. Four days later they drew 3-3 at home to Fulham in the Premier League under spookily similar circumstances.
Arsenal built another two-goal lead Wednesday and held onto it this time. In fairness, Montpellier had already been eliminated from the competition and had little incentive to attack.
Even so, the visitors created little and Arsenal ended the match comfortably in control. Arsenal will face tougher tests in the coming weeks, but a clean sheet in European competition will help build confidence for the defense.
Arsenal have scored in seven consecutive matches in all competitions, a run dating to the back-to-back losses to Schalke and Norwich in October. In their last four matches, the Gunners have scored 12 times, an average of three per contest.
That's a nice number, and the unit as a whole appears to be coming together.
Losing Robin van Persie to Manchester United obviously served as a devastating blow to Arsenal's attack. As the season has progressed, however, his replacements—note the plural form—have steadily improved.
As of Wednesday, Lukas Podolski and Olivier Giroud have combined for eight goals and four assists in the Premier League and four goals and five assists in the Champions League (stats via WhoScored.com here and here).
Van Persie has tallied eight goals and three assists in the Premier League and three goals and no assists in the Champions League (stats via WhoScored.com here).
Those comparisons reflect well on Podolski and Giroud, who admittedly have taken time to settle into Arsenal's team. Van Persie's loss was indeed devastating, but as the season progresses, Arsenal are becoming a team with multiple potent threats on offense.
Jack Wilshere returned from his long-term injury layoff in October and had generally played well since then. Wednesday he turned in a strong performance capped by a fine opening goal.
The goal can be seen here.
As this team continues to carve out its identity in the post-RvP era, Wilshere continues to command more influence on the pitch. He demonstrated his value Wednesday with a team-high rating of 8.61 at WhoScored.com.
Wilshere's return has been a feel-good story for Arsenal supporters this season. Moving forward, the young Englishman will play an increasingly vital role in the Gunners' fortunes.
725 - Days since Jack Wilshere last scored a competitive goal for Arsenal (27/11/2010 against Aston Villa). Relief.— OptaJoe (@OptaJoe) November 21, 2012
Arsenal started sloppily. In the midfield, Jack Wilshere, Santi Cazorla and Mikel Arteta all struggled to string together passes. As a team, Arsenal struggled to hold possession.
Gradually the hosts asserted themselves on the game. Defender Laurent Koscielny hit the crossbar with a powerful header in the 11th minute, and Lukas Podolski came close twice in the first half.
But it was only after halftime that Arsenal truly took control. Wilshere's goal helped calm nerves, and Podolski's impressive strike made the final 27 minutes a formality.
By the final whistle, Montpellier had managed only one shot on target. Despite looking dangerous on the counter, the visitors rarely created real chances.
Arsenal won comfortably in the end, and though there were anxious moments in the group stage, qualification was secured with a match to spare.
Now, can the Gunners show a sustained run of form in the league?