Leicester will not be given a Champions League reprieve if Chelsea win their final against Manchester City next week.
The Blues had seemed set to crash out of the top four with a 2-1 defeat to Aston Villa at Villa Park on Sunday, with former Chelsea youngster Bertrand Traore opening the scoring for Villa just before the break.
Anwar El Ghazi then added a second for Dean Smith's men from the penalty spot in the second half.
That result could have let Leicester in for a spot in the Champions League if they beat Tottenham, but the Foxes went down to a 4-2 defeat.
Jamie Vardy scored a couple of penalties for Leicester, but strikes from Harry Kane, an own goal from Kasper Schmeichel and a brace from Gareth Bale secured victory for Spurs, who qualify for the new Europa Conference League.
Liverpool beat Crystal Palace 2-0 at Anfield to finish third in the table, with Sadio Mane scoring either side of half-time to secure a comfortable win.
Under competition rules, the Premier League would have had five teams in next season's Champions League if Chelsea had finished fifth but beat City in next week's final, while the Blues would have dropped into the Europa League if they'd finished fifth and lost in Porto.
FA Cup winners and fifth-placed finishers Leicester join West Ham in the Europa League, with Tottenham finishing seventh and playing in the new Europa Conference League.
