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Arne Slot's side took the lead through Harvey Elliott's early opener before Yasin Ayari equalised at the Amex Stadium.
Dominik Szoboszlai restored Liverpool's advantage just before the interval, but Brighton staged a late fightback as Kaoru Mitoma levelled before Hinshelwood came off the bench to net with his first touch.
Liverpool have taken just one point from their three matches following the title-clinching rout of Tottenham on April 27.
The Reds have lost at Brighton and Chelsea and squandered a two-goal lead in a draw with Arsenal since their record-equalling 20th English crown was confirmed.
They can now look forward to receiving the Premier League trophy in Sunday's season finale against FA cup winners Crystal Palace at Anfield before an open-top bus parade through the city 24 hours later.