Fermin Lopez scored a brilliant hat-trick, Marcus Rashford added two more and Lamine Yamal netted from the spot as the Catalan side overwhelmed the 10-man Greek visitors.
Lopez opened the scoring early, finishing from close range after Yamal's shot was parried. He doubled the lead on 37 minutes, latching onto a pass from Dro Fernandez before curling a low shot into the corner.
Olympiacos briefly threatened a comeback early in the second half. Ayoub El Kaabi converted a penalty via the post after a VAR check ruled Eric García had handled the ball in the area. But just minutes later, Santiago Hezze was shown a second yellow card for catching Marc Casado with an arm, leaving the visitors with 10 men.
The Blaugrana took full advantage. Yamal made it 3-1 from the penalty spot after Rashford was fouled. Rashford himself added the fourth with a low finish inside the box, and Lopez completed his hat-trick with a powerful strike from the edge of the area.
Rashford rounded off the scoring with a slick touch and drilled finish from the top of the box, sealing Barca's biggest Champions League win since their famous 6-1 comeback against PSG in 2017.
The result puts Barcelona on six points from three games, while Olympiacos remain winless and bottom of the group.
Youri Tielemans admitted Manchester United were lacking in every department after their shocking 4-1 Champions League defeat to Como in Italy on Wednesday, which extended their winless run to seven matches.
Manchester United endured a humiliating European evening against Como, suffering a comprehensive 4-1 defeat that intensified the scrutiny surrounding manager Michael Carrick.
Paris St-Germain produced a thrilling performance to defeat Barcelona in the Champions League, ending the Spanish side's 11-match unbeaten start to the season with a 4-2 victory at the Parc des Princes.
Manchester City demolished AEK Athens 5-1 in a Champions League encounter at the Etihad Stadium on Tuesday night with Phil Foden sublime as he netted a hat-trick.
