It was the first time Leverkusen made it through a two-legged Champions League knockout tie since they reached the final in 2002, when they lost 2-1 to Real Madrid.
The 2024 German double winners will face either Premier League leaders Arsenal or German champions Bayern Munich, who eliminated Leverkusen at the last 16 stage last season.
Leverkusen had not conceded at home in any competition since early January and were rarely troubled by the energetic but toothless Greek champions.
Olympiacos rested six starters in their Greek Super League match on Saturday in the hopes of reaching the Champions League last 16 for the first time since 2013-14, when they were narrowly eliminated by Manchester United.
