The hosts battled to victory to head into the final two games before the knock-out stage begins with a three-point cushion in second place.
The Greek champions’ home record in the competition had included seven wins from its previous 10 games, but it had to rely on an impressive display from ex-Benfica goalkeeper Roberto to pick up three points Tuesday and make second place their own in Group D.
The two-time European Cup champions initially looked more threatening, but Olympiakos took the lead 13 minutes in as the visiting defenders failed to pick up the run of Kostas Manolas, who headed home Jose Holebas’ corner.
Benfica continued to look the more dangerous of the two sides, but found Roberto in inspired form.
The 27-year-old pulled off numerous saves to keep Olympiakos in the lead, but the visitors’ finishing left a lot to be desired as they continually wasted great openings, while the hosts offered little in attack.
Benfica made four changes from the side that drew 1-1 with the Greek side in their last Champions League match, with talented teenager Lazar Markovic among those returning.
Olympiakos head coach Michel made only two alterations from the teams’ last meeting, former Benfica man Javier Saviola coming back in together with Sambou Yatabare.
Visiting coach Jorge Jesus insisted beforehand that the hostile atmosphere in Greece would not affect his players and their start supported his claims as both Oscar Cardozo and Markovic forced Roberto into saves in the first 10 minutes.
Despite Benfica’s good start, the hosts took the lead against the run of play in the 13th minute as Holebas’ corner was headed in powerfully by the unmarked Manolas.
Benfica should have drawn level two minutes before the break, but Nemanja Matic completely missed the ball when Ezequiel Garay headed a corner back towards the six-yard box.
Jesus’ side started the second half similarly well, but again Roberto denied it as Markovic saw a volley from the edge of the area parried away by the on-loan Atletico Madrid man.
The anxiety of Olympiakos’ fans became more apparent as the match approached the hour mark and in the 57th minute Benfica left-back Silvio broke into the area, only to then deliver a feeble effort that Roberto palmed away.
Enzo Perez flicked the ball over his head four minutes later before unleashing a volley towards the bottom corner, but Roberto was equal to the task once again.
Benfica pressed with determination in the final stages and with 10 minutes left former Olympiakos youth player Filip Djuricic skipped past two men before firing at goal, but Roberto clawed his effort away, ensuring the Greeks go three points clear of Jesus' side.