The Blues came from behind on three separate occasions to claim the win after extra time.
This resilience drew special praise from Di Matteo after the match:
“It’s a good feel factor when you win,” The Chelsea manager told SkySports.
“It was a very exciting game, a typical cup game which was quite open, and we played very, very well.
“We had a lot of chances. We could have finished of the game much earlier than we did, and once again, we showed what fantastic character to come back three times from behind.”
“It’s a fantastic dressing room in there – we never give up. We showed it tonight and on Sunday when we went down to nine men and ten men.”
Ryan Giggs gave the visitors the lead after 20 minutes, but Blues’ defender David Luiz levelled the scores from the penalty spot shortly after.
United again took the lead on the verge of half-time, but Gary Cahill cancelled out Javier Hernandez’s effort.
Nani’s 59th minute strike looked to be enough to decide the tie, but Eden Hazard converted from the spot to make it 3-3 at the end of normal time.
Daniel Sturridge and Ramires put the Londoners 5-3 up in extra-time before Giggs pulled back a consolation goal late on.