Greco and Mitroglou struck in the final 10 minutes to seal the second successive victory over their French Group B rivals.
Paulo Machado's early goal handed Olympiakos a fourth minute lead before Montpellier levelled the score in the 66th minute with a Younes Belhanda penalty.
The Greeks took their total to six points to stay third, two behind leaders Schalke 04 and one adrift of Arsenal.
Olympiakos got off to a dream start by taking the lead after just four minutes following a penetrating run by left-back Jose Cholebas. The Greek international's cross was turned on to the post by Mitroglou but Machado was on hand to tap home the rebound.
Montpellier barely threatened the Schalke goal in the first half, with Souleymane Camara's mis-directed lob their best effort.
Gaetan Charbonnier replaced Remy Cabella at half-time as Montpellier boss Rene Girard looked to bolster his attack and the visitors finally started to put some pressure on the home side when keeper Roy Carroll rushed out to block substitute Jonathan Tinhan's shot.
Joris Marveaux then headed straight at the Northern Irishman from close range before the visitors were given the opportunity to equalise from the penalty spot after Camara was felled in the box by Djamel Abdoun. Belhanda confidently slotted home the spot-kick.
Olympiakos went 2-1 ahead with 10 minutes left when Greco rifled home after Montpellier failed to clear a corner.
Mitroglou then sealed the three points two minutes later with a close range finish from another Cholebas cross.
