Liverpool shattered Tottenham's hopes of finishing in the Premier League's top four with a 4-2 win that left Aston Villa on the brink of Champions League qualification despite their 1-0 defeat at Brighton on Sunday.
Needing a win at Anfield to close the gap on fourth-placed Villa, Tottenham slumped to a fourth successive loss to leave their Champions League hopes in tatters.
Villa are seven points ahead of fifth-placed Tottenham, who have a game in hand but will miss out on the top four if Unai Emery's men win one of their remaining two matches.
Mohamed Salah was back in the Liverpool team after being dropped for last weekend's draw at West Ham.
The Egypt forward had argued with Klopp before being introduced as a substitute at the London Stadium and fanned the flames afterwards when he said there would be "fire" if he spoke about the clash.
Klopp, in the final weeks of his nine-year reign, was celebrating in the 16th minute when Salah notched his 25th goal in all competitions this term with a clinical header from Cody Gakpo's cross.
Andrew Robertson scored Liverpool's second on the stroke of half-time as the Scotland left-back finished from close-range after Salah's shot was saved by Guglielmo Vicario.
There was worse to come for woeful Tottenham as Gakpo headed in a 50th-minute cross from Harvey Elliott, who netted the fourth in the 59th minute with a superb curler from 20 yards.
It was little consolation for Tottenham that Richarlison reduced the deficit in the 72nd minute before setting up Son Heung-min's goal five minutes later.
Third-placed Liverpool's first victory in three league games kept them in mathematical contention to win the title, but in truth they have little chance, with leaders Arsenal five points ahead with only two games left.
A Villa win combined with a Tottenham loss would have sealed a Champions League place for Emery's side.
But Villa were unable to fulfil their part of that equation as Joao Pedro's 87th-minute goal condemned them to a second painful defeat in four days.
'It's in our hands'
Ending Brighton's six-match winless run, Pedro headed in the rebound after Robin Olsen saved his penalty, which had been awarded for Ezri Konsa's foul on Simon Adingra.
Surprisingly beaten 4-2 by Olympiakos in the Europa Conference League semi-final first leg on Thursday, Villa were well below their best once again.
Emery's men host Liverpool and travel to Crystal Palace in their last two games as they fight to return to the Champions League for the first time since 1982-83.
"We competed but we didn't get a good result and we didn't deserve more. I don't want to know anything about Tottenham because it's in our hands," Emery said.
At Stamford Bridge, seventh-placed Chelsea thrashed West Ham 5-0 to keep alive their hopes of European qualification
Chelsea boss Mauricio Pochettino is fighting to convince the club's co-owner Todd Boehly to give him a second season in charge after his troubled debut campaign.
Pochettino admits it is "not his decision" if he stays, but securing a place in Europe could be enough to avoid the sack.
Cole Palmer put Chelsea ahead in the 15th minute with his 21st league goal of the season, the forward firing home after West Ham failed to clear.
Conor Gallagher doubled Chelsea's advantage after 30 minutes with a blistering volley after West Ham's Kurt Zouma deflected the ball towards the midfielder.
Noni Madueke bagged Chelsea's third six minutes later as the winger turned in Thiago Silva's header from close-range.
Nicolas Jackson piled on the misery for woeful West Ham in the 48th minute and the Senegal striker bagged his second with 10 minutes left.
AFP