The 32-year-old is now Liverpool’s fourth top scorer ever with 229 goals.
His brace took him past Billy Liddell, with only Ian Rush (346), Roger Hunt (285) and Gordon Hodgson (241) ahead of him.
Salah’s latest heroics only underlined the urgency to get his future resolved, with the forward’s current deal due to expire at the end of the season.
He is free to sign a pre-contract agreement with foreign clubs from January and has hinted several times that this could be his last season at Anfield.
With Salah scoring 18 times in all competitions, Liverpool have been on fire since Slot arrived from Feyenoord to replace Jurgen Klopp in the close-season.
Klopp delivered Liverpool’s last Premier League title in 2020 and it looks increasingly likely Slot will emulate that success in his maiden campaign.
The Reds have won 21 of their 25 matches in all competitions under Slot and have a game in hand on Chelsea to strengthen their lead in the title race.
This was a remarkable display of Liverpool’s firepower as Luis Diaz and Alexis Mac Allister scored to put them in command.
Dominik Szoboszlai grabbed Liverpool’s third just before the interval and Salah took over after the break before Diaz netted again.
Punished for Ange Postecoglou’s insistence on sticking to his high defensive line, it was the first time in 10 years that Tottenham had conceded five or more at home in a Premier League game.
An eighth league defeat this season leaves Tottenham languishing in 11th place as the pressure mounts on Postecoglou.
Earlier, Manchester United crashed to a humiliating 3-0 home defeat to Bournemouth, while Chelsea missed the chance to go top of the league after a 0-0 draw at Everton.
Manchester United captain Bruno Fernandes reacts in his side's defeat to Bournemouth. Photo / AFP
United boss Ruben Amorim, who once again left Marcus Rashford out of his squad, is set for a miserable Christmas following the worst result of his brief reign.
Languishing in 13th place, United have suffered four defeats in nine matches in all competitions since Amorim arrived from Sporting Lisbon in November to replace the sacked Erik ten Hag.
United’s second successive loss after their League Cup exit at Tottenham on Thursday underlined Amorim’s belief that their road back to the top will be long and arduous.
United, who have conceded first in their last six games, were booed off at half-time, while the final whistle was greeted by more jeers from the few fans who stayed until the bitter end.
While it is far too early to pass judgement on Amorim, the Portuguese coach cannot afford many more results like this if he is to keep the players and fans on his side.
Amorim’s decision to play without Rashford for the third consecutive game will face fresh scrutiny after United’s wretched performance.
Amorim surprisingly omitted the 27-year-old England forward from the squad for United’s win at Manchester City last weekend, prompting Rashford to hint he was willing to leave the club for a “new challenge”.
Rashford was at Old Trafford wearing a United tracksuit amid his extended exile as Amorim made six changes from the line-up beaten 4-3 by Tottenham in the League Cup quarter-finals.
Again, United were exposed at set-pieces in the 29th minute when Bournemouth’s teenage defender Dean Huijsen punished poor marking at a free-kick to glance a header past goalkeeper Andre Onana.
There was even worse to come for Amorim in the second half as Justin Kluivert doubled fifth-placed Bournemouth’s advantage with a 61st minute penalty following Noussair Mazraoui’s foul on the forward.
Antoine Semenyo compounded United’s misery two minutes later with a cool finish from Dango Ouattara’s pass.
Second-placed Chelsea could have gone top, for at least a few hours, if they had won at Everton.
But Enzo Maresca’s side had to settle for a goalless stalemate that ended their five-match winning run in the league.
Chelsea sit one point behind Liverpool who have two games in hand on the Blues.
It was an encouraging start to a new era for Everton - four points clear of the relegation zone - under new owners the Friedkin Group, whose purchase brought an end to Farhad Moshiri’s tumultuous tenure.
Wolves boss Vitor Pereira enjoyed a dream debut as his side won 3-0 at relegation rivals Leicester.
Replacing the sacked Gary O’Neil, Pereira made an immediate impact after leaving his role at Saudi Pro League side Al-Shabab.
Goncalo Guedes started the Pereira era with a flourish as he met Nelson Semedo’s cross with an agile finish in the 19th minute.
In the 36th minute, Rodrigo Gomes slid in to notch his first goal for Wolves before Matheus Cunha’s 44th minute strike ensured third-bottom Wolves would move within two points of fourth-bottom Leicester.
Bottom-of-the-table Southampton held on for a 0-0 draw at Fulham as new manager Ivan Juric watched from the stands.
Juric, axed by Roma in November after just 12 games, was not in charge on Sunday as he awaited a work permit to replace Russell Martin.
Southampton are eight points adrift of safety with only one win from 17 league games.