But the Dutchman’s succession of Jurgen Klopp continues to look flawless after a 23rd win in 27 matches in all competitions.
Slot was able to recall Diaz, who had been rested for the 3-1 win over Leicester on Boxing Day, and it was the Colombian who opened the floodgates on 30 minutes at the London Stadium.
Diaz’s intended pass into Curtis Jones rebounded back into his path off a West Ham defender and he dispatched his shot low into the corner.
Mohammed Kudus was inches away from an equaliser when his effort came back off the post. But another heavy home defeat puts Hammers boss Julen Lopetegui back under pressure after a four-game unbeaten run.
Two goals in four minutes just before half-time killed the game as a contest. Salah’s delightful turn helped tee up Gakpo to roll in his ninth goal in 14 games.
The Egyptian then curled in at Alphonse Areola’s near post, with some help from the West Ham goalkeeper, to hit the 20-goal mark for the eighth consecutive season since joining Liverpool in 2017.
Speculation over Alexander-Arnold, Salah and Virgil van Dijk’s futures has not derailed Liverpool’s flying start under Slot.
All three could discuss a move to a foreign club on a free transfer next season within days, but remain focused for the moment on winning a second Premier League title together.
Rumours over Alexander-Arnold’s potential move to Real Madrid have resurfaced again in the Spanish media over the past week and the England international showed why he is a man in demand with a thunderous strike that deflected in off Max Kilman.
Jota’s appearance as a substitute was further evidence of the extra firepower Liverpool enjoy over their title rivals.
The Portuguese set the seal on a dominant win with the finish for the fifth goal, but had another sumptuous Salah assist to thank for it.
Salah jinked his way beyond three West Ham defenders before laying the ball to Jota for his 13th Premier League assist of the season to go with 17 goals in 18 games.
Defending champions Manchester City travelled to the King Power drained of confidence after just one win in all competitions since late October.
Their frailties over the past two months, which resulted in nine defeats in their previous 13 games, were on display again.
But Savinho’s first-half goal and an Erling Haaland header after the break earned a much-needed three points.
Leicester provided a stern test and might feel they could have got something out of the match as Facundo Buonanotte hit the post and Jamie Vardy missed a key chance at 1-0 down.
City’s bid for a fifth straight title looks to be over as they are 14 points behind leaders Liverpool, who have played one game fewer. But the result lifts them to fifth in the table and within striking distance of the top four.
Savinho opened the scoring midway through the first half with his first goal for City while Haaland secured the win in the 74th minute - sparking wild celebrations among the City players.
Leicester remain rooted in the bottom three after losing their past four games under new manager Ruud van Nistelrooy.
Nuno Espirito Santo’s Forest beat Everton to win their fifth straight Premier League match, leapfrogging Chelsea and Arsenal.
Chris Wood chipped over Jordan Pickford for the opening goal in the 15th minute after being set up by Anthony Elanga.
Wood turned provider for Forest’s second, which came just after the hour mark when Morgan Gibbs-White lashed home to make it 2-0.
Spurs were on course for just their second Premier League win since late November against Wolves.
Hwang Hee-chan scored an early opener for the visitors but were ahead for just five minutes before Rodrigo Bentancur headed an equaliser.
Brennan Johnson powered Spurs into the lead in the dying minutes of the first half to put his side on track for all three points.
But Jorgen Strand Larssen produced a brilliant finish from the angle to earn Wolves a share of the points.
New Wolves manager Vitor Pereira remains unbeaten, with two wins and a draw in his first three matches in charge at Molineaux, taking the club out of the relegation zone.
Crystal Palace won just their second home league game of the season, seeing off bottom club Southampton 2-1, thanks to goals from Trevoh Chalobah and Eberechi Eze.
Dango Ouattara scored an 89th-minute leveller as Bournemouth drew 2-2 at Fulham.
