A David Ngog brace helped Liverpool go straight to the top of Group K after being made to work for a 4-1 win over Steaua Bucharest.
The Reds were forced to enter the Europa League in the third qualifying round after finishing seventh in last season's Premier League and had to overcome Rabotnicki and Trabzonspor to make it to the group stage.
Joe Cole gave Liverpool a dream start as he opened the scoring against Steaua Bucharest after just 28 seconds.
But the Romanian visitors drew level when Cristian Tanese latched onto a Bogdan Stancu through-ball in the 13th minute to equalise against the run of play.
The Reds regrouped to regain the lead through a 56th-minute penalty by Ngog before late goals by substitute Lucas Leiva and Ngog saw the English giants ease home.
Ngog's double made it five goals in five games for the French striker so far in this season's competition.
The other group game saw Italian outfit Napoli held to a 0-0 draw at home to Dutch side FC Utrecht.