Liverpool set up a dramatic final-day battle to qualify for the Champions League with a vital 3-0 win at Burnley, while Tottenham's bid to reach the Europa League suffered a blow in a 2-1 defeat against Aston Villa on Wednesday.
Jurgen Klopp's side moved into fourth place in the Premier League thanks to goals from Roberto Firmino, Nathaniel Phillips and Alex Oxlade-Chamberlain.
Liverpool are above fifth-placed Leicester on goal difference, with the Reds on +24 and the Foxes on +20.
If Liverpool win their final game at home to Crystal Palace on Sunday, they should finish in the top four and salvage a difficult campaign that saw them tamely surrender the title to Manchester City.
Leicester host Tottenham on Sunday, while third-placed Chelsea, one point above Liverpool, travel to Aston Villa.
Firmino put Liverpool on course for their fourth consecutive victory with a clinical finish from Andy Robertson's 43rd minute cross.
Phillips got the second goal in the 52nd minute with a header from Sadio Mane's cross for his first goal for the club.
Oxlade-Chamberlain lashed in Liverpool's third in the 88th minute.
"We had to win the 'semi-final' and we did. Nothing is decided yet but we improved our position and we have the final," Klopp said.
"That's what we needed. It's what we deserve because this was a top performance."
Fifth and sixth place finishes secure a spot in next season's Europa League, while seventh place brings entry into a play-off for the new Europa Conference League.
Tottenham will have to wait until their last game of the season to discover their European destiny.
A second defeat in their last three games left them in seventh place, level on points with eighth-placed Everton and three points behind sixth-placed West Ham.
They will have to beat Leicester and hope West Ham lose to Southampton to pip their London rivals on goal difference.
Harry Kane was named in Tottenham's starting line-up just days after reportedly telling the club he wants to leave.
The England captain is keen to move on as he chases the first trophies of his career, with Manchester City, Manchester United and Paris Saint Germain among the clubs linked with the striker.
Tottenham fans in the 10,000 crowd urged Kane to stay as they chanted "Harry Kane, he's one of our own" before kick-off.
- Hammers eye Euro berth -
Tottenham's Steven Bergwijn was making his first league start since February and the Dutch winger celebrated his return with a superb strike in the eighth minute.
But Tottenham's lead lasted only 12 minutes as Sergio Reguilon sliced Marvelous Nakamba's cross into his own net.
Villa punished more sloppy Reguilon defending in the 39th minute when Bertrand Traore pressured the defender into surrendering possession, allowing Ollie Watkins to fire home from close-range.
Tottenham were booed off at full-time, but Kane applauded fans on all sides of the stadium in a gesture which may have served as his farewell.
"He means a lot. He's a Tottenham player," caretaker boss Ryan Mason said.
"I'm very disappointed with the result. It wasn't how we wanted to finish the season in front of our fans."
West Ham are on course to qualify for the Europa League after a 3-1 win at relegated West Bromwich Albion.
The Hammers started badly as Declan Rice hit the post with a third minute penalty before Matheus Pereira's corner was flicked into his own net by Tomas Soucek in the 27th minute.
But Soucek equalised in first-half stoppage time, setting the stage for Angelo Ogbonna and Michail Antonio to score in the final eight minutes.
David Moyes' side know a draw in their last game against Southampton will secure European football.
After the match, West Brom boss Sam Allardyce confirmed he will leave at the end of the season.
Everton remain in the hunt for the Europa Conference League after Richarlison's 48th minute header sealed a 1-0 win against Wolves.
Arsenal won 3-1 at Crystal Palace and could still qualify for the Europa Conference League as they battle to avoid missing out on European football for the first time since 1995-96.
Nicolas Pepe's 35th minute volley put Arsenal ahead before Christian Benteke equalised in the 62nd minute.
Arsenal forward Gabriel Martinelli netted in stoppage-time before Pepe struck again with virtually the last kick.
With their season finale against Brighton to come, ninth placed Arsenal sit one point behind Tottenham and Everton.
Newcastle beat relegated Sheffield United 1-0 thanks to Joe Willock's header just before half-time.