It looked as though the game was heading for a draw after Heung-min Son cancelled out Mohamed Salah’s opener, but Roberto Firmino’s brilliant late header ensured all three points for Jurgen Klopp.
Premier League champions Liverpool headed into the contest in first place, though Jose Mourinho’s Spurs sat second only by virtue of goal difference.
The hosts had the better of the early spell, though there was an element of fortune about their goal as Salah’s shot deflected wickedly off Toby Alderweireld and looped into Hugo Lloris’ net off the post after 28 minutes.
With Liverpool confident and pushing forward, Spurs looked in trouble sitting deep – but they were level five minutes later through Son.
Giovani Lo Celso played a delightful through-ball to split the Liverpool defence, and Son beat Alisson Becker with a cute near-post finish – with the goal given following a tight VAR review for offside.
Both sides had plenty of chances to find a winner after the break as Klopp and Mourinho went for the win: Steven Bergwijn shot wide and later hit the post, while Harry Kane headed wide when unmarked at a corner.
At the other other, Salah almost scored another before Sadio Mane saw an effort crash off the bar.
But Liverpool’s quality in front of goal told as Firmino rose highest to power a header into the top corner in the 89th minute.