Joel Matip and Sadio Mane scored in a 2-1 win over Aston Villa to keep Liverpool's quadruple hopes alive.
A point behind Manchester City at the top of the table, Pep Guardiola's side know they can win the title if they win their final three games, starting with Wolves on Wednesday night.
However, Douglas Luiz opened the scoring on his 100th Premier League appearance, putting Liverpool a goal down inside three minutes.
The visitors responded quickly through Matip. Three minutes later, after Virgil van Dijk's effort was saved, his centre-back partner tapped home from close range.
Both Villa and Liverpool missed easy chances, and without Mohamed Salah, Luis Diaz, Diogo Jota, and Sadio Mane were left to try and score.
It was Diaz who eventually scored the game's 15th Premier League goal, the Senegalese heading home from six yards after his teammate's inch-perfect cross.
The Reds' three points keep the pressure on City, but Klopp will be hoping Fabinho is fit for Saturday's FA Cup final against Chelsea after being forced off with a hamstring injury in the first half.