Harvey Elliott applied the finishing touch to a lovely move to put the Premier League champions ahead early on, though that goal was equalised by Yasin Ayari in minute 32.
Dominik Szoboszlai made it 2-1 in favour of the Reds on the stroke of half-time but the Seagulls fought back again in the second period to snatch all three points through a pair of their substitutes.
Kaoru Mitoma levelled proceedings after an hour had been played before Jack Hinshelwood netted an 85th-minute winner with his first touch.
Team news
Federico Chiesa made his first start in the Premier League and was one of four changes to the line-up deployed at home to Arsenal.
Kostas Tsimikas, Jarell Quansah and Elliott also came into Arne Slot’s line-up.
Alisson, Konate, Szoboszlai (Jones, 63), Salah, Chiesa (Nunez, 63), Gakpo (Diaz, 63), Elliott, Tsimikas, Gravenberch, Quansah, Bradley (Endo, 77).
Unused subs: Kelleher, Gomez, Van Dijk, Robertson, Alexander-Arnold.
First half
Liverpool’s opener could have arrived even earlier than it did, with Cody Gakpo curling just wide inside 60 seconds and then Mohamed Salah forcing a save from Bart Verbruggen.
Their bright start was rewarded with nine minutes on the clock, though, when Elliott nudged home Conor Bradley’s cut-back.
The full-back raced past two challenges after receiving a lovely flick from Salah, who himself was found by Szoboszlai’s sensational crossfield switch.
With that goal, Slot’s men became the only side in the club’s history to score in every one of their league fixtures on the road in a single campaign.
