Spain striker Fernando Torres doubled the advantage with a fine solo effort after captain Steven Gerrard had opened the scoring on four minutes, following up after his penalty was kept out by Marseille goalkeeper Steve Mandanda.
UEFA Champions League: Complete Coverage
Marseille, who had stunned Liverpool 1-0 at Anfield in October, looked nervous from the kickoff and will have to be content with finishing third in the group and continue in the UEFA Cup.
Marseille, the 1993 European champions, started the match with a perfect 6-0 home record against English clubs in European club competitions but their hopes were short-lived on a cold, windy night.