Liege beat Greeks to remain in hunt
Dieudonne Mbokani fired the ball home from a tight angle in the 30th minute after Olympiakos defender Olof Mellberg failed to clear a seemingly harmless through-ball.
As the visitors searched for an equaliser, Milan Jovanovic pounced to double his side's lead with a simple header three minutes from time.
Liege's victory leaves them two points behind second-placed Olympiakos on four points. With two rounds remaining, Arsenal top the group with 10 points after beating Dutch side AZ Alkmaar 4-1.
"We knew we needed this win to keep our European football hopes alive and Belgium's European football hopes alive," Liege goalkeeper Sinan Bolat told reporters.
"We have been unlucky up to now and we knew we could win this game if we played as well as we have been doing."
Bolat stood firm in tight game by blocking out most of the attacking opportunities created by the visitors who lost their influential winger Luciano Galletti just before halftime through injury.
Liege continued to search for a second goal and went close from a couple of corner kicks in the second half before Jovanovic finally headed home late in the game.