It has been a more tortuous passage than anticipated but United have finally become the first English team to qualify for the last eight of the European Champions' Cup since Liverpool in 1985, the year of Heysel.
They reached the quarter-finals, where they will play Porto in March, by virtue of succeeding in Vienna while Fenerbahce failed in Turin. However, they will need to improve considerably on their Champions' League form if they are to beat the Portuguese club.
Last night's contest was littered with errors but adorned by a glorious goal from Ryan Giggs after 23 minutes. It was created by Eric Cantona who then capped one of his best performances for United in Europe with a second goal after 71 minutes.
David Beckham made that one. Once again he was United's best player. But everyone played a part, especially Peter Schmeichel who kept United in the game with a stunning save while the match was still in the balance.
United's joy was tempered by injuries to Roy Keane, Nicky Butt and Gary Neville. Keane's looked especially serious. He is believed to have had 30 stitches in a deep gash that cut down to the bone. The Irishman was also booked along with Ole Gunnar Solskjaer. Both will be eligible to play Porto.
It was United's first away win, and Cantona's first goal, since their last European jaunt, to play Fenerbahce in Istanbul seven weeks ago.
United's success was the second notable Mancunian triumph in the Ernst Happel Stadium. Twenty-six years ago, in front of just 10,000 spectators, Manchester City defeated Gornik Zabrze, of Poland, to win the European Cup-Winners' Cup.
This time there were more than 40,000 spectators including a healthy travelling contingent from England. They saw United take early control. Gary Pallister was commanding in defence and Solskjaer lively in attack but it was the midfield which was the key. They harried and hustled forcing Rapid to waste possession. Once the ball was won they moved sharply, looking to attack at every opportunity.
This early dominance should have been rewarded as early as the fifth minute. Beckham broke down the right and crossed, the ball dipped over Solskjaer for Giggs to volley with his favoured left foot. However, he lifted his head too early and the ball went over. Three minutes later a dipping volley from Neville seemed destined for goal but Michael Konsel tipped it over.
For a quarter of an hour United held sway. Then Rapid burst into life as if startled from a deep slumber. The catalyst was a long ball from Peter Schottel which Schmeichel, far from his area, just reached ahead of Rene Wagner.
A minute later Schmeichel denied Wagner again, diving low to his right to brilliantly push a header away.
Still they came. Wagner, now on the left, brushed past Pallister and crossed low to Christian Stumpf. Schmeichel got there first but could not hold the ball, it fell to Dietmar Kuhbauer who, faced with an empty goal, blasted over.
A bad miss, but nothing like the one which followed. Cantona crossed and Schottel inexplicably headed straight to Solskjaer four yards out. The Norwegian should have scored his first goal away from Old Trafford but he steered it wide.
A goal had to come - and it came to United. Giggs beat his man in the centre circle and found Cantona. He turned Trifon Ivanov and fed Giggs who had continued his run. As Konsel came out Giggs guided the ball past him.
Konsel denied Nicky Butt, Cantona and Solskjaer before United went into the break to learn that Michele Padovano had put Juventus ahead in Turin. They were probably not told that Fenerbahce had hit the bar first, an event which underlined the knife-edge they trod.
Their own position should have been eased within a minute of the restart as Solskjaer set up Giggs from eight yards. Incredibly the Welshman added his name to the litany of misses by side-footing wide.
Konsel made a double save from Butt, Cantona hit the post, Beckham shot wide. Eventually Beckham got free on the right and Cantona timed his run perfectly to turn the ball in at the far post.
A delighted United manager, Alex Ferguson, said: "We played very well, we showed good composure. Schmeichel's save was fantastic, that's the kind of save that makes him the best. That five-minute period showed us that they could be dangerous but once we weathered the spell I thought we would be all right.''
United's performance was the perfect riposte to the Rapid Vienna coach, Ernst Dokupil. In the match programme he had selected an all-star XI from Group C. Despite seeing his own team overwhelmed at Old Trafford in September he had not picked any United players. "Their stars," he said, "had not lived up to expectations." They have now.
Manchester United (4-4-1-1): Schmeichel; G Neville (Casper, 89), May, Pallister, Irwin; Beckham, Butt (Poborsky, 80), Keane (McClair, 76), Giggs; Cantona; Solskjaer. Substitutes not used: Cruyff, Pilkington (gk).
Rapid Vienna (3-5-2): Konsel; Schottel, Ivanov, Zingler; Prosenik, Heraf, Kuhbauer, Stoger (Mandreko, 61), Ratajczyk; Wagner, Stumpf (Penksa, 62). Substitutes not used: Jovanovic, Guggi, Hedl (gk).
Referee: L Sundell (Sweden).
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