Tottenham threatened to dent Liverpool's title chances with an equaliser at Anfield.
The Reds dominated the first half at Anfield and took an early lead through Roberto Firmino.
Andy Robertson picked out the Brazilian in the box with a fine cross and Firmino made no mistake with his header.
Tottenham needed to improve after the break and they did as Mauricio Pochettino tweaked his system.
Harry Kane had forced Alisson into a fine save as Spurs threatened. before they levelled in controversial circumstances.
Gary Neville spots Liverpool tweak to take advantage of Tottenham weakness
The England skipper was felled by Jordan Henderson before taking a quick free-kick.
Kane's pass found Kieran Trippier down the right and his cross eventually found Lucas Moura at the back post and the Brazilian made no mistake.
Replays of the incident proved inconclusive, with Liverpool fans suggesting the ball was still moving when Kane made the pass and should have been ruled out by Martin Atkinson.
Liverpool fans criticise "greedy" Mohamed Salah after key moment vs Tottenham
Sky Sports commentator Gary Neville suggested Atkinson had given Kane the advantage.
He said: "It was a wonderful switch of play from Kane from the free-kick. Is the ball moving? Maybe, but he gets the benefit of the doubt.
"It’s a brilliant move from Spurs and Son’s run takes Matip away and leaves that space."
Fortunately for Liverpool, the Lucas goal was not decisive as they snatched the win.
Mohamed Salah's header was parried by Hugo Lloris but the ball struck Toby Alderweireld and rolled into an empty net.
City went back to the top as they beat Fulham 2-0 at Craven Cottage on Saturday.
Pep Guardiola's men must still go to Old Trafford while Liverpool's toughest game is against Chelsea .
