Marseille, which went into the game with a 6-0 record against English teams at home, only needed a tie to advance, but it never had a chance.
Liverpool was up 2-0 after 11 minutes on goals by captain Steven Gerrard and Spaniard Fernando Torres, and it put the game away on Dutch forward Dirk Kuyt's goal early in the second half. Dutch winger Ryan Babel completed the rout in added time.
The victory was the third straight in the Champions League for Liverpool, which had started the group stage with two losses and a tie. The Reds have scored 16 goals in the three wins.
Next up for Liverpool manager Rafael Benitez is a meeting with the club's American owners, Tom Hicks and George Gillett, who are flying to meet with Benitez Sunday -- the day of the Reds' game against Manchester United -- to discuss possible player moves over the winter. Sunday's meeting follows some sharp exchanges between Benitez and his bosses over club policies.
"I was not thinking about my own situation, just about the match," said Benitez. "We can play against anyone, it's not a problem. We have a lot of confidence now."
For Marseille, its exit from the Champions League comes after it finished with three straight losses after opening with wins over Besiktas and Liverpool and a tie with Porto.
"It's a catastrophe for everyone," said Marseille coach Eric Gerets.
The former Belgian international replaced Albert Emon as Marseille coach in September after OM got off to a poor start in the French league.
"We totally missed that match," Gerets added, "which is a pity because we had looked good in the previous ones."