Antonio Conte's goal with less than five minutes remaining saved Juventus' blushes in Athens where a 1-1 draw with Olympiakos secured a 3-2 aggregate win for the Italians, who are still on course for a fourth straight final appearance.
Sinisa Gogic had scored early on for the Greeks before a passionate home crowd.
Two Andrei Shevchenko goals allowed Dinamo Kiev to end Real Madrid's reign as European champions and give the Ukrainians a place in the semi-finals 3-1 on aggregate.
Elsewhere, Bayern Munich, whom United have said they would prefer to avoid in the semis, completed a crushing 6-0 aggregate win over Bundesliga champions Kaiserslautern with a 4-0 away victory achieved with goals from Stefan Effenberg, two from Carsten Jancker and another from Mario Basler.
In Kiev, John Toshack could only look on aghast as Real Madrid gave up the title they won 10 months ago in Amsterdam at the expense of Juventus as Shevchenko underlined his reputation as one of the most lethal finishers in Europe.
He came precariously close to being the villain of the piece as Real keeper Bodo Illgner saved his 62nd minute spot kick, awarded after the German veteran upended the Ukrainian striker in the area.
But Shevchenko reacted quickest to poke home the rebound and rounded off a superb individual performance 10 minutes from the end with a second goal from close range after a perceptive through ball from equally dangerous strike partner Sergei Rebrov.
In Athens, Juventus once again diced with death, as has become their habit in recent seasons, before seeing off unlucky Olympiakos as the veteran Conte's late strike saved them from a defeat on away goals.
Conte's intervention was cruel on Olympiakos, who had levelled the aggregate scores early on before controlling large parts of the game.
Conte pounced to steer the ball home after Olympiakos goalkeeper Dmitris Eleftheropoulos fumbled the ball under pressure from striker Filippo Inzaghi.
Juventus had made things hard for themselves in the first leg in Italy. It only took Olympiakos 12 minutes of the second encounter to level the aggregate scores. Yugoslavian international Predrag Djordjevic found acres of space on the left flank and curled in a left-wing cross which found Yugoslav-born Cypriot international Gogic, who planted a firm header past Juve keeper Michelangelo Rampulla.
Bayern Munich are meanwhile warming up for an assault on a fourth European Cup, having not won the trophy since their three consecutive triumphs between 1974 and 1976.
Bayern unceremoniously dumped Kaiserslautern in front of 31,200 disillusioned home fans. With their 2-0 cushion from the first leg a fortnight ago, Bayern shut the gate after just eight minutes when a controversial incident decided the course of the evening.
Kaiserslautern's Hungarian defender Janos Hrutka jostled and pulled at the shirt of Bayern's goal-ward-bound striker Carsten Jancker who threw himself to the turf inside the area.
"That was no penalty, I mean does he have to throw himself to the ground like that?" asked Kaiserslautern's trainer Otto Rehhagel. The resulting penalty was safely converted by Effenberg as Hrutka took an early shower. Bayern exploited the situation and punched holes in the opposition's defence, which relied far too often on ineffective offside traps. That was the case for the second goal when unmarked French international Bixente Lizarazu drove down the wing, drew the only Kaiserslautern defender in the area and gave Jancker a simple header after 22 minutes.
Jancker's second goal in the 39th minute revealed just how much the luck of the Gods is on Bayern's side right now. The tall crew-cut striker had the ball nipped off his boot by a sliding defender but it struck the leg of Kaiserslautern's striker Uwe Rosler and squirted out at right angles over the head of Andreas Reinke and into the net.
Bayern rested Effenberg and Jens Jeremies after the break but were still able to score a fourth goal through a deflected Basler free kick in the 56th minute.
