Jurgen Klopp is headed for a fairytale end to his tenure at Anfield as the Reds took advantage of both of their title rivals losing points.
Liverpool were forced into action by Brighton as Roberto De Zerbi, one of the contenders to replace Klopp, caused the German plenty of problems once again.
But for the first time in five matches, Klopp got the better of the Italian thanks to goals from Luis Diaz and Mohamed Salah.
The Reds have the relative comfort of hosting bottom-of-the-table Sheffield United in midweek before ramping up their run-in with another trip to Manchester United next weekend.
Just three weeks ago, Liverpool's quadruple bid ended in thrilling fashion at Old Trafford as United won 4-3 in the FA Cup quarter-finals after extra time.
A local derby away to Everton could also prove tricky, while they face Champions League chasing Tottenham and Aston Villa in two of their last three matches.
Upcoming fixtures:
4 April: Sheffield United (H)
7 April: Manchester United (A)
14 April: Crystal Palace (H)
20 April: Fulham (A)
24 April: Everton (A)
27 April: West Ham (A)
4 May: Tottenham (H)
11 May: Aston Villa (A)
May 19: Wolves (H)