Goals in either half from Georginio Wijnaldum and Alex Oxlade-Chamberlain secured the Reds’ third consecutive win in the section.
With Napoli and Salzburg drawing 1-1 in the other group game, the result at Anfield lifted Jürgen Klopp’s side to the summit.
A victory against Napoli in the next Champions League fixture – at home on Wednesday November 27 – would guarantee Liverpool a place in the last 16 as group winners.
A draw in that match would also be enough to send the Reds through if Salzburg do not claim three points from their trip to Genk on the same evening.