Liverpool came to London with five straight Premier League games without a win.
Three of them in January.
Jürgen Klopp's men had not scored a single goal in the league in 2021.
Roberto Firmino broke the sad suite when he scored 1-0 from close range in stoppage time in the first half.
Trent Alexander-Arnold gave the away team a superb start to the second half.
He fixed 2-0.
Tottenham reduced immediately when the Dane Pierre-Emile Höjbjerg thumped the ball next to Alisson.
Sadio Mané got the last word in the match when he set the final score 3-1 after just over an hour of play.
Four in the Premier League
It was Liverpool's first three Premier League goals in 2021 and also the first win in the league.
The team is in fourth place, four points behind Manchester City.
City have played one game less at the time of writing.
Tottenham are sixth in the league.
Striker Harry Kane, second in the Premier League shooting league, stepped down injured after the first half.