In extra time there was only one winner. Daniel Sturridge and Ramires put the hosts 5-3 up before a late Giggs penalty ensured a tense last minute.
Here, Sports Mole analyses the thrilling encounter to work out how it eventually went right for Chelsea.
On target 14
On target 9
Was the result fair?
In the end, yes. Chelsea did have the stronger team on the field as Roberto Di Matteo brought his star players off the bench and in the end they were too strong. Both sides were incredibly sloppy at times and many of the goals were gifts, but as Chelsea grew into the game from the second half onwards there was only likely to be one winner.
Good in attack, poor at the back. United's first two goals were directly from errors by the hosts, with Oriol Romeu, Peter Cech and David Luiz culpable. At the same time, however, Victor Moses was a constant threat, with Juan Mata and Hazard becoming increasingly confident as the time wore on.
Apart from some huge errors at the back, it was a good showing from an almost entirely different XI. They were clinical in attack during the initial 90 minutes and but for some increasingly poor defending that would have been enough for them. As it was, the two young centre-backs Michael Keane and particularly Scott Wootton could not deal with Chelsea's attack.
Sports Mole's man of the match
Anderson: It's close, but it has to be Anderson, who pips Moses. The United midfielder had to ask to be subbed off late in the second half but he had a good excuse to be out of breath. He pressured Romeu into a mistake for the opener and threaded Hernandez through beautifully for United's second. He also had a big say in Nani's goal. In all, his contribution was as big as anyone's, despite ending on the losing side.
This has to go to poor Wootton. United looked to have held on to another 3-2 win before Wootton took away Ramires's legs in the box as he shaped to shoot. He made a bigger error for Chelsea's fourth, but this one was more costly as Hazard rolled in a penalty for a last-gasp normal-time equaliser.
Lee Mason was too card happy. He started waving his yellow in the 12th minute, which set a precedent he had to follow. After that point almost anything amiss was booked. That said, he got all the penalty decisions right, bar one that he could have given to Chelsea for handball against Wootton.
Chelsea: Chelsea travel to Wales for a tough fixture against Swansea, who knocked out League Cup holders Liverpool tonight.
United: United host Arsenal on Saturday afternoon, who themselves are fresh from their 7-5 win over Reading. However, don't expect so many goals to be leaked as it will be a full-strength United who line up at Old Trafford.