The Greek champions went ahead on 13 minutes at the Georgios Karaiskakis stadium when slack Atletico marking at a corner allowed young French defender Arthur Masuaku to drill home a low shot.
It got even better for the hosts just after the half-hour mark when Ibrahim Afellay doubled the advantage.
Mario Mandzukic pulled a goal back for Atletico seven minutes before halftime, but the visitors fell behind again to Kostas Mitroglou’s 73rd-minute strike – his first goal for 10 months.
Atletico substitute Antoine Griezmann set up a tense finish with a close-range strike with four minutes left, but Michel's team clung on for victory.
After a tentative opening, the hosts went ahead from the first real chance of the match when Alejandro Dominguez’s short corner was teed up by Afellay for Masuaku, who beat Jan Oblak with a superb low strike from just outside the area.
Atletico fought back but striker Mandzukic was wasteful in front of goal and the Spanish side were punished against the run of play when Afellay put the hosts 2-0 ahead.
The goal came courtesy of a determined run from Dominguez, whose cross was dummied by Mitroglou. The ball broke for Afellay, who finished clinically into the bottom corner.
Atletico clawed their way back into the match when Mandzukic found the target, escaping the attentions of Eric Abidal to head home Cristian Ansaldi’s precise cross.
Olympiakos restored their two-goal lead when Mitroglou superbly controlled Pajtim Kasim’s cross, before swivelling to fire past Oblak from close range.
It was the striker’s first goal since he netted for Greece in their World Cup playoff against Romania last November.
Substitute Griezmann struck from Koke’s superb cross to set up a nervy final few minutes, but the hosts held on to claim the points amid jubilant celebrations following the final whistle.
(Editing by Justin Palmer and Toby Davis)
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