Jurgen Klopp's side go top of the Premier League and bounce back from a 2-0 defeat to Atalanta in the Champions League on Wednesday.
Liverpool started brightly but it was Brighton who had the first big chance after 10 minutes as Aaron Connelly went through on goal but missed the target.
Liverpool thought they took the lead before the break when Mohamed Salah scored but VAR correctly ruled the goal out for offside.
Jota broke the deadlock on the hour mark when he skipped past two defenders and slotted the ball into the far corner.
The Portugal international has now scored nine goals in all competitions since joining the club from Wolves.
Mane had a header ruled out for offside late on before Gross' penalty scored rescued a point for the hosts.