The Reds drew first blood on 17 minutes when Andrew Robertson picked out Roberto Firmino, who needed no second invitation with a towering header past Hugo Lloris.
The hosts threatened a second a minute later, but Trent Alexander-Arnold’s half-volley from a high ball flew off target.
Spurs were in sixes and sevens on all fronts, and a right-footed curler from Sadio Mane on 36 minutes narrowly missed the top corner.
Spurs drew up a positive reaction in the second half, and on 56 minutes Alisson Becker pulled down to push a Harry Kane shot to safety.
Serving a touchline ban, Mauricio Pochettino instigated the game’s first change after 69 minutes in Hueng Min-Son for Davidson Sanchez.
A minute later, Liverpool’s resilience fell down when Lucas Moura sent Christian Eriksen’s follow-up pass from Kieran Trippier’s cross into an empty net.
The Merseyside giants searched for a way back moments later, but Lloris finger-tipped Alexander-Arnold’s left-footed shot for a corner.
Furthermore, Jurgen Klopp opted for two out and out strikers in the closing phase after the introduction of Divock Origi and Fabinho.
Spurs blew a big chance to go in front when Moussa Sisoko shot wildly off target after being played through by Kane with six minutes to go.
A minute into added time, Liverpool sealed the points after miscommunication between Lloris and Toby Alderweireld saw the latter poking the ball over the goal-line.