Harry Kane’s 17th topflight attack of this season put Spurs 1-0 ahead at St Mary’s before two goals in five second half minutes from Yan Valery and James Ward-Prowse earned Saints a fine win.
Spurs are 10 points behind leaders Manchester City with eight games remaining.
Leading through Dominic Calvert-Lewin’s goal, Everton keeper Jordan Pickford blatantly fouled Salomon Rondon after falling the ball at the forward’s feet.
Referee Lee Mason given a punishment but did not send Pickford off – and the protagonist atoned for his mistake by rescuing Matt Ritchie’s spotkick.
Richarlison doubled the Toffees’ guide before Rondon paid down the shortage, Ayoze Perez scoring twice in three minutes to secure an unbelievable victory.
Huddersfield’s debilitating Premier League demise lasted as Bournemouth’s Callum Wilson scored facing of England manager Gareth Southgate, who titles his most recent squad on Wednesday.
Ryan Fraser added that the second in the Cherries’ 2-0 win.
Leicester took the lead during Youri Tielemans, just for Togo international Floyd Ayite to equalise before Vardy’s doublecheck.
The Cottagers are 1-3 points from safety with eight games left.
Cardiff remain from the relegation zone despite a 2-0 win over West Ham – aims from Junior Hoilett and Víctor Camarasa earning Neil Warnock’s side that the points.
From early match, Crystal Palace’s poor home form continued with a 2-1 defeat by ferocious rivals Brighton at Selhurst Park.
Former Palace forward Glenn Murray, who was listed as a replacement on the teamsheet before Florin Andone was hurt in the warmup, put Brighton ahead – but Luka Milivojevic equalised from the penalty spot.
The Seagulls completed the league twice for the first time since 1983-84 during Anthony Knockaert’s sublime finish. Palace have lost eight of their 15 home league games this year.
Leaders Manchester City expect to move four points clear at the top of the table when they amuse Watford in the 17:30 GMT kickoff, while there are 3 matches on Sunday.