Rene Girard's side belied their woeful domestic form to boss much of an entertaining encounter, but a leveller from their captain and a late winner saw the visitors grab victory
The home side made a blistering start to the match, but despite playing some lovely football, Charbonnier's volleyed effort was La Paillade's only effort on target in the first-half. However, the 23-year-old summer signing nabbed his first goal for his new club right after half-time to put the hosts in the driving seat.
In an entertaining end-to-end contest, Montpellier threatened to stretch their lead only for Olympiakos' skipper Torossidis to nod home an equaliser. Late drama ensued with Mitroglou turning home a last-gasp winner to steal the spoils.
Although they currently lie 16th in the French top flight, Girard's Montpellier started the game confidently and set the tempo early on. Younes Belhanda served warning that La Paillade were keen to put their domestic woes behind them: the midfielder flashing a fierce drive just wide on the quarter hour mark.
French striker Anthony Mounier looked particularly lively for the Ligue 1 champions in the opening stages, but the 25-year-old blasted a decent chance over after an imaginatively-worked free-kick.
Olympiakos, on the other hand, did not resemble a side who have strung seven back-to-back victories together domestically: Leonardo Jardim's outfit looking shell-shocked by the classy start made by their hosts.
The Greek side offered no attacking threat whatsoever in the first 20 minutes, the tricky jinkings of Leandro Greco on the left offering the only early indication that they could cause their French opponents trouble.
It was no surprise therefore when Greco created Olympiakos' first chance of note: the former Roma winger nutmegging Benjamin Stambouli before whipping in a dangerous cross that Algerian striker Rafik Djebbour was close to converting.
Despite Jardim's side starting to settle, Montpellier remained firmly on the front foot with the interval approaching.
However, Montpellier coach Girard - watching from the stands due to a touchline ban received in their previous 2-2 draw with Schalke - must have been frustrated that his side were creating openings without testing Olympiakos' number one Roy Carroll.
As the French side's early bluster started to flag, the Greek visitors appeared to grow in confidence. The Red and Whites backline looked solid and their midfield men were looking to cause problems: Portuguese midfielder Paulo Machedo firing a long-ranger over as the Greek champions trained their sights.
After an attacking lull, however, Montpellier regained their verve and were close to taking the lead when striker Charbonnier latched onto John Utaka's cross to force a smart stop from Carroll.
The pressing question, as both sides emerged after the break, was whether Montpellier's brittle confidence would allow them to sustain the swagger they had shown first-half.
An emphatic answer was delivered just minutes after the break by Charbonnier, who followed up his own flick-on to bury a low volley past Carroll to score his first goal for the French outfit.
However, Charbonnier's delight was almost cut short immediately, his error near his own box aiding an Olympiakos attack that saw former Valencia midfielder David Fuster mangle a glorious headed opportunity.
With the visitors stung into action, the game see-sawed: the Greek champions showing far more attacking intent, with Greco still to the fore, but Montpellier continuing to threaten through the outstanding Remy Cabella, Belhanda and Utaka.
Just when the game seemed to be slipping away, however, Olympiakos' skipper Torossidis rose to the occasion: the right-back venturing forward and converting Jose Holebas' wicked inswinging free-kick at the second attempt on 76 minutes.
A tense final quarter followed, but the game somewhat petered out with so much at stake for both clubs - only for substitute Kostas Mitroglou to win the match at the death.
The scene is set for a humdinger of a contest on November 6 when Olympiakos host the return fixture - the Greeks looking to secure a place in the Champions League knock-out phase and Montpellier realistically now playing for a Europa league spot.