Olympiacos are in with a shout of reaching the last 16 of the Champions League as they head into half time with a one-goal lead over Malmo.
The hosts were first to threaten as midfielder David Fuster let fly from 25 yards in the fifth minute, forcing visiting goalkeeper Robin Olsen into a textbook save.
Olsen was called into action again one minute later, pulling off an impressive reaction stop to thwart Pajtim Kasami on the rebound at point-blank range.
Olympiacos broke the deadlock with 23 minutes played when a throw-in caused chaos in the Malmo box, and Fuster capitalised on the confusion by bundling the ball home at the far post.
The Greeks were in control for much of the first period, but suffered a scare in the 38th minute when Delvin N'Dinga almost headed into his own net following a Malmo throw.
With Juventus and Atletico Madrid goalless at the break in Group A's other fixture, the Greeks need the Spaniards to do them a favour in the second period.