Until Saturday, the only win Liverpool – now nine unbeaten against Spurs in the top flight – had managed this year was in an FA Cup replay against fourth-tier Plymouth Argyle, with defeats to strugglers Swansea City and Hull City along the way.
It is a run that has almost certainly scuppered their dreams of competing with Chelsea for top spot, but they brought Spurs' own bid down in flames with a stunning display.
Mauricio Pochettino's side were not at the races for the opening 30 minutes particularly and had survived a couple of nervy moments even before Mane broke the deadlock in the 16th minute.
He quickly added a second as Ben Davies was caught napping and the game could have been put out of sight before the break, but Hugo Lloris denied Mane a third with a fine save.
The visitors regrouped for the second half, but could do little to truly trouble a Liverpool side determined to keep a grip on three precious points – their first since defeating Manchester City on the final day of 2016.
The result means Liverpool have taken 16 points from a possible 24 against fellow top-six sides and they climb to fourth, back above Manchester United and one point behind second-placed Spurs.
Klopp's side were positive from the outset and it took some desperate defending from Tottenham to thwart the hosts when Philippe Coutinho looked for the bottom-right corner deep inside the box.
But the Reds made their dominance count when Mane grabbed a quickfire double, showing a cool head to lift the opener over Lloris despite being off balance having eluded Davies.
Just 138 seconds later, Mane finished off a goalmouth scramble after Adam Lallana and Roberto Firmino had been denied.
The former Southampton forward should have had a hat-trick by the 22nd minute, but he failed to beat Lloris after capitalising on a defensive error from Davies, who tried to make amends by teeing up Son Heung-min, though his shot was tame and easily saved.
Dele Alli then saw a goalbound effort diverted over the crossbar by stand-in defender Lucas Leiva, with Spurs beginning to show the kind of spark that had led them on a nine-match unbeaten run in the league.
Spurs were much better organised after the interval and Harry Kane hit the post, though the flag had been raised for offside against the England striker.
Joel Matip's header, which proved straightforward for Lloris, served as a reminder of Liverpool's threat, but the home side were mostly content to slow things down.
Tottenham had very little answer to that approach and, indeed, they still had to soak up some pressure, with Coutinho drilling wide from the edge of the box in one of the few chances of a second half that saw seven yellow cards.
Liverpool do not return to action until February 27, while Tottenham face Europa League and FA Cup matches in a bid to keep their hopes of silverware alive.
Meanwhile, Chelsea head to Burnley on Sunday knowing a win will move them 12 points clear, with Antonio Conte's side having dropped only 13 points all season.