Jamie Vardy converted two penalties to give Leicester 1-0 and 2-1 leads in the crunch Premier League clash and, with Chelsea losing 2-1 at Aston Villa, that would have been enough for Leicester to claim fourth spot.
But a 76th-minute own goal by keeper Kasper Schmeichel gifted Spurs an equaliser and Gareth Bale, possibly in his last game for Tottenham on loan from Real Madrid, rubbed salt into Leicester's wounds with two well-taken late strikes.
England striker Harry Kane, who could have also been playing his last game for the London club amid transfer speculation, struck Tottenham's first equaliser to take his league tally to 23 this season and win the Golden Boot award.
Just like last term when a Champions League qualifying spot looked to be theirs for the taking, this season's FA Cup winners Leicester finished in fifth place and will have to be content with a Europa League campaign.
Victory left manager-less Tottenham in seventh spot and the minor consolation of a place in the inaugural Europa Conference League -- UEFA's third-tier club competition.
Leicester won the FA Cup for the first time last weekend, but just missing out on a top-four spot, having occupied it for most of the year, was a hammer blow. The Foxes are on 66 points while fourth-placed Chelsea finished with 67 from 38 games.
COOL PENALTY
Vardy opened the scoring in the 18th minute with a calmly taken penalty after VAR correctly awarded the hosts a spot kick after Spurs defender Toby Alderweireld needlessly stuck out a trailing leg to trip the Leicester striker.
Kane levelled in the 41st when he swivelled to volley the ball past Schmeichel from close range.
Vardy restored Leicester's lead from the spot after tangling with Davinson Sanchez as he burst into the area and referee Anthony Taylor gave the penalty.
Again Vardy easily beat Spurs keeper Hugo Lloris and, with news of Chelsea losing at Villa, the 8,000 fans inside the King Power Stadium were in a celebratory mood.
But then everything went wrong.
Schmeichel tried to punch away an inswinging cross in the 76th minute but only managed to divert the ball into his goal.
Ten minutes later Kane was played through and rounded Schemeichel but after the angle became too tight he looked up to pick out the unmarked Bale, on as a substitute, who stroked home with his left foot.
The stuffing was knocked out of Leicester and Bale produced a moment of quality to waltz through the defence before flicking a shot against the post and converting the rebound, taking his total to 14 goals in all competitions for Spurs this season.
It was tough on Leicester who, until losing to Chelsea in midweek, had been in the top four since the start of the year. (Reuters)