The Athens outfit bagged the full three points, but will have to settle for a spot in the Europa League round of 32 nonetheless
David Fuster gifted the Greek champions a 1-0 lead before the interval, but Simon Kroon levelled the scoring around the hour mark. Alejandro Dominguez then restored Olympiakos' lead, only for Markus Rosenberg to make it 2-2 before Kostas Mitroglou and Ibrahim Afellay decided the game.
Michel made nine changes to his team ahead of kick-off, with Pajtim Kasami and Fuster both handed spots in the starting line-up.
And the Greek outfit would have been ahead after 10 minutes if not for Robin Olsen's superb double save.
After brilliantly parrying away Dominguez's drilled cross, the Swede somehow gathered Kasami's powerful close-range follow-up.
But Olsen could do nothing to prevent the hosts taking the lead 12 minutes later when Fuster bravely latched onto Kasami's flick-on to nod in at the back post.
The Spaniard received a trailing boot in the face from Pa Konate for his troubles, but recovered quickly enough as Olympiacos pressed for a second, with experienced playmaker Dominguez driving them forward.
However, it was Malmo who came close to an equaliser with just over five minutes of the half remaining when a long throw from Ricardinho hit the crossbar after deflecting off the head of Olympiacos midfielder Delvin Ndinga.
Olympiacos started strongly after the interval and Olsen denied Mitroglou's close-range flick with yet another terrific save.
Despite the increased pressure from the hosts, Malmo snatched a surprise leveller in the 59th minute when substitute Kroon slotted calmly past Roberto just two minutes after entering the fray.
Emil Forsberg broke swiftly down the right flank before curling in a pinpoint low cross to the feet of Kroon, who duly applied a deft finish into the bottom-right corner.
However, Olympiacos edged back in front just four minutes later through Dominguez's fantastic long-range strike.
The midfielder controlled the ball perfectly before executing a curling half-volley that sailed past Olsen and nestled into the left-hand corner.
But again Malmo hit back with nine minutes left through Rosenberg – who grabbed both goals in October's clash between the two sides – as he connected with Anton Tinnerholm's cross before side-footing home.
Olympiacos, though, made it 3-2 with just three minutes left when Mitroglou smothered home Dominguez's corner.
There was more late drama as the hosts finally had a two-goal cushion when second-half substitute Afellay was played in by Kasami and the Dutch winger finished coolly past Olsen.
Malmo's evening then went from bad to worse when Adu received his second yellow card for a nasty-looking stamp on Kasami, who had to be carried off on a stretcher.Tuesday's result sees the home side qualify for the Europa League round of 32, while Malmo end last in their group.