Leaders Leicester saw their nine-match unbeaten Premier League run ended by Liverpool substitute Christian Benteke's second-half winner.
The Reds dominated the first half at Anfield, but failed to fully test Foxes keeper Kasper Schmeichel.
They were rewarded when Roberto Firmino's pull-back from the left was steered in by a stretching Benteke.
Leicester offered little threat, Nathan Dyer going closest as they failed to score for the first time this season.