Inspirational defender Giorgio Chiellini said Juventus kept the dream alive thanks to a dogged, clinical display at Wembley where they never stopped believing.
Tottenham looked like they were heading for the last eight of the Champions League when Son Heung-min scuffed home the opening goal to put them 3-2 ahead on aggregate.
But the Serie A giants picked themselves up off the canvas and two goals in three second-half minutes from Gonzalo Higuain and Paolo Dybala turned the tie on its head.
Chiellini was superb as the visitors kept Spurs at bay for the final 20 minutes and afterwards the grizzly veteran toasted a gutsy performance.
"It was an amazing victory," he told RTÉ Sport.
"It was very difficult, but we knew before the match... Tottenham (have) fantastic players, fantastic strikers so surely we'd concede some chances - Kane, Alli, Eriksen. Amazing players, but we knew also that we would have a chance.
"I think it was a penalty (when Jan Vertonghen tripped Douglas Costa in the first half) for us but it's not important. The referee can't see it always in the right way but I want to think about our game.
"In the second half it was very difficult but we maintained the calm. It's a fantastic night. We continue our dream. This year it is more difficult than others because all the big teams are arriving at the quarter-final.
"Now, we're very happy for this amazing night."
A disappointed Spurs boss Mauricio Pochettino told BT Sport 2: "In less than three minutes we conceded two goals, (we made) two big mistakes - and that is why we are out of the competition.
"But at the same time I think we were in both legs, in both games we were the better team.
"We conceded and I think it was just two mistakes in the game. But they have quality and if you make a mistake they will score.
"I feel proud...we were the better team. Of course I'm disappointed but it is a part of growing.
"For us it was tough but a fantastic experience for us."