Jurgen Klopp's side are hoping to break the 100-point record established by Manchester City in 2018 and they remain on course after securing their first away win since February.
Liverpool have 92 points and need nine more from their remaining four games against Burnley, Arsenal, Chelsea and Newcastle to clinch the new record.
Mohamed Salah punished poor defending in the sixth minute, grabbing his 22nd goal of the season and Liverpool's first away from home since February.
Jordan Henderson increased Liverpool's advantage with a curling finish from the edge of the area three minutes later.
Leandro Trossard got one back with a powerful strike in first half stoppage-time.
But Salah's 76th minute header from Andrew Robertson's corner ensured Liverpool's five-match winless run on their travels came to an end.