Goals from Seydou Doumbia in the second minute and Gelson Martins just over 10 minutes later left the home side shell-shocked and created a platform for Sporting to take the points.
Bruno Fernandes added the visitors' third goal in the 43rd before two late second half goals from Olympiakos substitute Felipe Pardo made the scoreline more respectable for the hosts.
The result means that in a group in which Barcelona thrashed Juventus 3-0, Olympiakos already look vulnerable.
The lack of any adequate holding midfielders in their starting line-up and the sheer quality of Sporting cost the Reds dearly on the night.
The Greek team appeared more distracted at the start by the intimidating atmosphere inside the Georgios Karaiskakis Stadium than the visitors.
Barely 69 seconds after kickoff, the Olympiakos defence failed to clear a Marcos Acuna free kick from the right and Doumbia headed the ball home.
Sporting quickly made it 2-0 in a counter-attack after an Olympiakos corner, with Gelson beating goalkeeper Stefanos Kapino amid jeering by the home fans.
The problems in midfield continued for the Greeks, with Sporting twice hitting the woodwork through Bruno Fernandes and Gelson before Fernandes added Sporting’s third, outsmarting Kapino with the Reds’ defence conspicuously absent.
Sporting clearly dropped a gear at halftime, made some substitutions later on and Olympiakos asked some questions at the Portuguese goal in the second half.
Pardo finally cut the deficit with his left foot and deep in injury time the Colombian added a second that somewhat eased the suffering for the home fans.
While Sporting are off to a dream start, life is not going to get any easier for Olympiakos who must next visit Juventus on Sept.27.
(Reporting by Graham Wood; Editing by Ken Ferris/Rex Gowar)
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