Mane, whose absence at the African Nations Cup coincided with Liverpool's slump, scored in the 16th and 18th minutes and only Tottenham keeper Hugo Lloris prevented the Senegalese completing a first-half hat-trick as the visitors buckled.
"The reaction was perfect, it was an outstanding performance offensively in the first half and defensively in the second," Liverpool boss Juergen Klopp, whose side have crashed out of both domestic cups and fallen off the pace in the league, said.
Surprisingly beaten by struggling Hull City and Swansea City already this year, Liverpool once again showed that against the top sides this season they are a match for anyone.
In their matches against other members of the top six this season they have won four and drawn four.
Tottenham, unbeaten in their last nine league matches and with only two previous league defeats all season, could have been four or five goals down inside the opening half hour.
With Tottenham's defence wide open Mane put Liverpool ahead when he ran onto Georginio Wijnaldum's pass and held off Ben Davies to scoop a shot past Lloris.
Two minutes later he fired home a rebound after Lloris had denied Adam Lallana and Roberto Firmino in quick succession.
Mane was then twice denied by Lloris as Liverpool made a mockery of their supposed lack of confidence.
Simon Mignolet had to make one good save to deny Son Heung-Min but was largely untroubled as Liverpool cruised to victory.
Tottenham have now failed to win their last nine league matches against Liverpool, losing six, and their meek surrender left manager Mauricio Pochettino critical of his team.
"It is difficult to fight for the Premier League if you show that performance, that lack of desire to play for a win. If you start a game like we start then it is very difficult," he said.
While Chelsea can go 12 points clear on Sunday, Liverpool are right back in the mix in the battle for the top four.
Victory lifted Liverpool back into fourth spot with 49 points from 25 games, one behind second-placed Tottenham and third-placed Arsenal.
(Reporting by Martyn Herman, editing by Ed Osmond and Toby Davis)
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