In a victory reminiscent of so many which carried them to their first title in 30 years last season, the hosts’ relentlessness was rewarded when the Brazil international powered home a header from Andy Robertson’s corner with the seconds ticking down.
Spurs boss Jose Mourinho looked sickened, having assumed his side had done enough to earn the point which would have kept them at the summit.
It appeared they would be frustrated by a Mourinho game-plan which everyone predicted and which the Portuguese seemed satisfied enough with to replace midfielder Steven Bergwijn, who hit the post in the second half and looked a threat on the counter-attack, with left-back Sergio Reguilon with 15 minutes to go.
But Jurgen Klopp’s men have seen this sort of thing before and encouraged by their opponents’ passivity continued to drive forward and that eventually brought its reward.
How much the victory meant was evident as Klopp, having had words with Mourinho, raced onto the pitch at the final whistle and lifted Sadio Mane clean off his feet before embracing each and every one of his players before producing his trademark triple fist-pump for the supporters on the Kop.
Liverpool expected Tottenham to play on the counter-attack and that is what they did, although there was little in the way of attacking from the visitors as they conceded vast amounts of possession.
That tactic told in the 28th minute when the Reds’ midfield dominance saw Curtis Jones drive into the penalty area and when the ball broke loose Salah’s shot looped up off Toby Alderweireld and inside Hugo Lloris’ left-hand post.
The goal did not appear to change the direction of traffic but out of nowhere a trademark Tottenham counter caught Liverpool cold.
Son raced onto Giovani Lo Celso’s pass through the inside-left channel, in the space vacated by the advanced Trent Alexander-Arnold as the covering Jones switched off for fraction of a second, and slotted past Alisson Becker with VAR confirming he had just stayed onside.
Liverpool had only themselves to blame having found Lloris with virtually every shot on target as Firmino (twice), Salah and Mane all made it too easy for the France international when well placed, although the ball hitting Eric Dier’s arm in the penalty area was not even deemed worthy of a VAR check.
Tottenham finished the half with just 21 per cent possession but still on level terms. Klopp ended it by launching a tirade at the officials before haring off down the tunnel the second the whistle was blown.
Just 28 seconds after the break Premier League debutant Rhys Williams missed his header, his first mistake of the night, and Bergwijn screwed wide a chance to give Spurs a surprise lead.
Liverpool had come out sloppy and when Alisson kicked straight to Harry Kane, the Brazil goalkeeper had to back-pedal quickly when the ball was lobbed back at him.
Spurs were playing a more open game and after a Salah shot from distance was tipped around the post by Lloris, Bergwijn hit the upright at the other end from Son’s flick-on and Kane missed a simple header by burying it into the turf and watching it bounce over the crossbar.
Another Kane mistake, this time losing possession inside the centre-circle to Williams, saw Salah shoot tamely at Lloris again, with Mane drilling a drive against the crossbar.
With 15 minutes remaining, Mourinho seemed to settle for a point and that just persuaded Liverpool to push forward for the remainder of the game and their endeavour and ambition was rewarded with Firmino’s late intervention.