Spurs, leading 1-0 on the night and 3-2 on aggregate through Son Heung-min’s goal, were half an hour from reaching the quarter-finals and proving that finally they belong among Europe’s heavyweights.
But two goals in three minutes from Gonzalo Higuain and Paulo Dybala floored Mauricio Pochettino’s side as their European run finally came to a halt with a 4-3 aggregate defeat.
It was a brave display from Spurs, who came agonisingly close to forcing extra time when Harry Kane hit a post with a minute to play, but Champions League glory will have to wait for another year at least.
Having battled back from two goals down to secure a 2-2 draw in the first leg in Turin last month, Tottenham knew a clean sheet would be enough to finish the job and add Juve to the scalps of Real Madrid and Borussia Dortmund.
Yet Spurs were never likely to sit back and in a breakneck start from the hosts, Son had a snap-shot palmed out by veteran keeper Gianluigi Buffon with the rebound just evading Kane and Dele Alli.
Kane then surged past Giorgio Chiellini and rounded Buffon only to uncharacteristically find the sidenetting, albeit from an admittedly tight angle.
Tottenham had a major let-off when Douglas Costa raced past Jan Vertonghen and was clearly tripped by the Spurs defender, but to the disbelief of the Juve players Polish referee Szymon Marciniak gave nothing.
Meanwhile, Son had been riled by a tangle with Andrea Barzagli, who trod on the forward twice as he lay on the floor following a barge in the back.
He exacted revenge six minutes before half-time, moments after drilling a shot across goal and wide after being sent through by Alli.
That looked a big miss, but barely 30 seconds later the South Korean made amends, arriving at the far post to convert a low cross from Kieran Trippier.
It was not the cleanest of strikes, Son scuffing the ball into the turf before it spun and looped in between Chiellini and Buffon, but it elicited the almighiest of roars around Wembley.
Juve now had 45 minutes to save their European season – and in the 64th minute they gave themselves a chance.
Higuain, the man who should probably have put the first leg out of Tottenham’s reach but for some poor misses, this time made no mistake when he hooked in Sami Khedira’s header at the far post.
And barely three minutes later Juve had turned the tie on its head, Dybala – who missed the first leg through injury – racing through onto Higuain’s pass and dispatching his shot across the exposed Hugo Lloris into the net.
Spurs tried to rouse themselves again but found Chiellini in their way, the defender whipping the ball from Kane’s foot as he went to tap in Son’s cross.
Son was inches wide with a curler before Kane’s header came back off a post and bounced on the line, only to be hacked clear by Barzagli in a dramatic finale which spelled heartbreak for Spurs.
