Leandro Trossard scored a hattrick for the Seagulls to cancel out a brace from Roberto Firmino and an own goal by Adam Webster during the 3-3 draw.
With Klopp leaving Diogo Jota, Darwin Nunez and Luis Diaz all on the bench, the visitors took the early initiative and went ahead in the fourth minute before Trossard got his and his team’s second in the 17th minute.
Liverpool woke up after conceding twice and Roberto Firmino got the first of his two goals in the 33rd minute before levelling the contest early in the second half to set up tense final moments.
The home side then completed the comeback when Webster inadvertently put the ball into his own net in the 63rd minute.
Just when it seemed that Liverpool will sneak away with a win, Trossard completed his hattrick in the 83rd minute with an assured finish to steal a deserved point for his side.
Liverpool came into the contest against Brighton trailing Premier League leaders, Arsenal, by a whopping 12 points and the draw leaves them a fair way off in their quest for a second league title under Klopp.
With their next two games in the league against Arsenal and Manchester City, things could get even worse for the Reds.
Meanwhile, in other contests across England, Chelsea earned their first win under Graham Potter against Crystal Palace as Conor Gallagher struck late to seal a 2-1 win.
Everton, Newcastle and West Ham also earned wins.
Earlier in the day, Arsenal defeated Tottenham 3-1 for North London Derby bragging rights.