Steven Alzate's second-half goal secured a first league win for Brighton & Hove Albion at Anfield since 1982 that dealt a blow to Liverpool's title defence.
Mohamed Salah struck a shot over early on after a superb through-ball by Jordan Henderson.
But the champions were largely subdued while Brighton impressed, with Neal Maupay and Dan Burn both going close.
On 56 minutes, Alzate gave Brighton a deserved lead. Burn headed back across goal and Alzate combined with Leandro Trossard to steer the ball into the net.
A confident Brighton threatened to double their lead through chances for Trossard, Burn and Maupay.
Roberto Firmino's shot high and wide summed up the night for Liverpool, who suffered a second successive home defeat.
They are fourth on 40 points, seven behind leaders Manchester City, having played a match more.
Brighton are 15th with 24 points.
Liverpool: 7 Feb v Man City (H)
Brighton: 6 Feb v Burnley (A)
Referee: Kevin Friend. Assistants: Simon Beck, Adrian Holmes. Fourth official: Paul Tierney. VAR: Simon Hooper. Assistant VAR: Derek Eaton.