Graham Potter's Brighton were excellent from start to finish and recorded their third Premier League win four matches to lift them up to 15th and away from the relegation zone.
The all important goal arrived on 56 minutes as Solly March delivered a ball to the far post and Dan Burn did superbly to head the ball back into the danger zone and Steven Alzate finished off for his first goal in the Premier League for Brighton.
Brighton were the better team and almost made it two when Pascal Gross forced a fine low save from Kelleher.
Scroll down and click through see how the players rated.
9. Dan Burn 7/10
A hugely eventful match. Played at left wing back and the 6ft 7in defender was a threat in the Liverpool box. Missed the best chance of the first half when he hit his right footed effort over from eight yards. His header then teed-up Alzate for his goal after the break
10. Neal Maupay 8/10
Very few chances but played so well for the team. Ran the Liverpool defence ragged and linked the play well with Trossard and Alzate. Replaced by Connolly on 83
11. Adam Lallana 6/10
Came on for the injured Solly March and used his experience to close out the game. Very clever in possession against his former club
12. Aaron Connolly 6/10
Came on for the last 10 for Maupay and used his pace to try and stretch the defence