Manchester City briefly jumped above the Reds in the table with victory at Crystal Palace.
Raheem Sterling scored twice and Gabriel Jesus got the third in a 3-1 win at Selhurst Park to send City top by a point.
But Liverpool got top spot back after Sadio Mane and Mo Salah goals got them over the line against Chelsea.
Liverpool are now two points above City, but have played a game more.
That game in hand is a tricky one though – away at neighbours Manchester United later this month.
Defeat for Chelsea leaves them fourth in the table, two above United, and one behind Tottenham, who are third.
Arsenal will go above both sides if they defeat Watford tomorrow night.
Premier League scores
Friday April 12
Leicester 0-1 Newcastle
Saturday April 13
Tottenham 4-0 Huddersfield
Brighton 0-5 Bournemouth
Burnley 2-0 Cardiff
Fulham 2-0 Everton
Southampton 3-1 Wolves
Manchester United 2-1 Wolves
Sunday April 14
Crystal Palace 1-3 Manchester City
Liverpool 2-0 Chelsea
Premier League fixtures
Monday April 15
Watford v Arsenal (8pm)