Spurs, who won the first leg 1-0 and progressed after the tie finished 4-4 on aggregate, will play Ajax Amsterdam for a place in the final against Liverpool or Barcelona after one of the most remarkable matches in the competition's history.
The hosts claimed the goal that put them ahead in the tie just before the hour as De Bruyne released Aguero with a sublime throughball. The Etihad erupted, but within five minutes the home side were 2-1 down with Son Heung-Min - scorer of the only goal in the first leg - netting twice on the counterattack. A lovely strike from a hard angle gave Pep GUARDIOLA some breathing room.
And Eriksen says he is one lucky man from that night, having gave up the ball away to the build-up to what would have been Sterling's tie victor and hat-trick as well.
A late VAR call ruled out a last-gasp victor from Sterling, as Spurs survived long enough to shock their Premier League rivals and advance to the semi-finals.
Rather than sit back and play the game out, City went for the kill.
Xbox One S All Digital gaming console launched: Price, features and availability
Microsoft is giving Xbox customers something they've been asking for over the past couple years: Xbox Game Pass Ultimate . They'll also miss out on Xbox One backward compatibility, unless those titles are made available digitally.
"We missed a penalty in the first leg but I am so proud of the players and the fans", Guardiola said. The Brazilian displayed his frustration on the VAR decision at the end of the match which turned the tie on its head by deeming Raheem Sterling's would-be 93rd minute victor to be offside.
"It was a rollercoaster, we gave them a lot but also got a lot it was a weird game".
A thundering strike from Aguero in the 59th minute put City in the driving seat again but it was stunned in the 73rd minute when Spurs substitute Fernando Llorente bundled in a Kieran Trippier corner to restore the London club's advantage through away goals.
Jurgen Klopp's men appear to have the kinder run-in, with City travelling to Old Trafford for a Manchester derby after completing their Spurs trilogy.
Owing to Llorente's contentious goal, Tottenham managed to level the tie against their mighty opponents. The Champions League, the biggest prize of all, continues to elude City's owner, Sheikh Mansour bin Zayed al Nahyan.
The final whistle saw a visibly crestfallen Guardiola who went straight off the bench to the dressing room after another season of European disappointment, while Spurs' team celebrated. My players are heroes to be here.