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The Argentine, who has led Spurs to three successive top-three finishes in the Premier League, has penned fresh terms to keep him in north London until 2023.
West Brom still need a fortunate combination of results elsewhere to take their fight into the final day at Crystal Palace.
Tottenham Hotspur edged closer to a third consecutive season in the Champions League by opening up a five-point lead on fifth-placed Chelsea.
Premier League: Chelsea, in fifth, are hard on Tottenham Hotspur's heels in the battle for a top four finish.
Spurs took an early lead on Saturday through Dele Alli but Jose Mourinho's men hit back with goals from Alexis Sanchez and Ander Herrera.
Goals from Alexis Sanchez and Ander Herrera cancelled out Dele Alli's opener and ensured that Tottenham's decade-long wait for a trophy continues.
Victory kept Chelsea's outside chances of chasing down Tottenham Hotspur for a place in next season's Champions League alive.
Harry Kane stepped up his bid to win the Premier League's golden boot as Tottenham warmed up for the FA Cup semi-finals with a 1-1 draw at Brighton on Tuesday.
Manchester City host Swansea next but could even be confirmed as champions as early as Sunday if Manchester United lose to rock bottom West Brom.
Christan Eriksen's wonder strike levelled in first-half stoppage time, before Alli took centre stage to end a barren run by his standards with two smart finishes just after the hour mark.
Spurs sit five points above the English champions in the fourth and final Champions League place with just eight games of the campaign to go.
Manchester City boast a 16-point lead over Manchester United and could seal the league against their local rivals at the Etihad next weekend.
Mauricio Pochettino said that his star striker Kane had made remarkable progress.
Chelsea, beaten by Arsenal in the final last May, are eyeing a return to the title match after winning 2-1 at Leicester.
Goals from Romelu Lukaku and Nemanja Matic helped Manchester United beat Brighton 2-0.
Harry Kane limped off with his side trailing 1-0 at Bournemouth on Sunday, before Pochettino's men bounced back to win 4-1
Tottenham Hotspur move above Liverpool into third in the Premier League, but it was a bittersweet victory with concerns over Harry Kane's fitness.
Tottenham's third successive league win lifted them five points clear of fifth-placed Chelsea in the race to qualify for next season's Champions League via a top-four finish.