Manchester United and Newcastle are on the brink of qualifying for next season's Champions League after Liverpool's 1-1 draw against Aston Villa, while Everton remain in relegation danger despite their dramatic 1-1 draw at Wolves on Saturday.
United's 1-0 victory at Bournemouth, combined with Liverpool's failure to beat Villa, left Erik ten Hag's men and Newcastle within touching distance of ensuring Premier League top four finishes.
Fourth-placed United and Newcastle, in third, are both three points clear of fifth-placed Liverpool, who have only one game left.
Newcastle can seal their spot with a draw or win against Leicester on Monday or Chelsea on May 28.
United take their turn at securing the lucrative top four place against Chelsea on Thursday and Fulham next weekend.
Liverpool's final game of the season is against relegated Southampton, but although they have a superior goal difference to United if they finish level on points, they are likely to have to settle for a place in the Europa League.
At the Vitality Stadium, United took the lead in the ninth minute when Casemiro spun to meet Christian Eriksen's cross with an acrobatic bicycle kick from close-range.
United were unbeaten in their previous 134 league matches when leading at half-time and that remarkable sequence continued as they held firm after the interval.
At Anfield, Liverpool boss Jurgen Klopp was watching from the stands as he served a touchline ban following his recent rant about referee Paul Tierney.
Villa wasted a 22nd-minute penalty when Ollie Watkins fired wide after the striker was brought down by Ibrahima Konate.
Despite Watkins' miss, Unai Emery's team went ahead in the 27th minute through Jacob Ramsey's volley from Douglas Luiz's cross.
Roberto Firmino and James Milner, set to leave Liverpool at the end of the season, came on for their Anfield farewells in the closing stages.
And it was Brazilian forward Firmino who rescued a point with his close-range finish in stoppage-time.
- Everton drama -
Yerry Mina's last-gasp equaliser boosted Everton's hopes of avoiding playing in the second tier for the first time since 1954.
Sean Dyche's men fell behind after 34 minutes when Adama Traore's shot was pushed out to Hwang Hee-chan, who netted from close-range.
Mina bundled in Everton's leveller nine minutes into stoppage-time to leave the fourth bottom Toffees two points above the relegation zone.
Third bottom Leeds would go above Everton with a win at West Ham on Sunday, while second bottom Leicester would also leapfrog Dyche's team if they beat Newcastle on Monday.
Tottenham's season to forget hit a new low with a 3-1 home defeat against Brentford.
Ryan Mason's side took the lead through Harry Kane's 28th league goal this season, but a Bryan Mbeumo brace and Yoane Wissa's late strike left them floundering in eighth place.
Frustration has mounted throughout the final weeks of a troubled season for Tottenham and fans hung banners outside the stadium pointing the finger of blame at owners ENIC.
One banner changed the "E" in the 'ENIC OUT' slogan to a £ sign, while another had pictures of several of the club's departed managers, including this season's victims Antonio Conte and Cristian Stellini, labelling them as "innocent" while ENIC were described as "guilty".
In another sign of the angst at Tottenham's owners, fans sent black balloons floating down onto the pitch throughout the match while chairman Daniel Levy sat stone-faced in the directors' box.
Fulham and Crystal Palace shared a 2-2 draw at Craven Cottage.
Later on Saturday, Arsenal will look to delay the Premier League title party for champions-elect Manchester City.
An Arsenal defeat at Nottingham Forest would hand City their fifth title in six seasons.
Even if the second-placed Gunners win in Nottingham, City will still clinch a third successive title if they beat Chelsea on Sunday or defeat Brighton or Brentford in their final two games next week.
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