Ryan Giggs gave the visitors a 22nd-minute lead after a sloppy pass from Petr Cech allowed the Welshman to net, but David Luiz levelled with a powerful spot-kick following Alexander Büttner’s foul on Victor Moses.
Another Chelsea defensive error led to Javier Hernández’s clinical finish just before half-time, yet the Blues responded again, with Gary Cahill scoring from a corner.
Nani’s superb solo effort in the 59th minute appeared to seal the Red Devils’ progress, but Eden Hazard scored from the spot in added time to give Chelsea a dramatic reprieve.
And Di Matteo’s men set up a quarter-final tie against Leeds United courtesy of extra-time goals from Daniel Sturridge and Ramires, with Giggs scoring a consolatory penalty on the stroke of full-time.
“It’s a good feel factor when you win,” Di Matteo told Sky Sports.
“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 off the game much earlier than we did, and once again, we showed our fantastic character to come back three times from behind.”
“It’s a fantastic dressing room here – we never give up. We showed it tonight and on Sunday when we went down to ten men and nine men.”
Leeds United v Chelsea
Swansea v Middlesbrough
Norwich v Aston Villa
Bradford City v Arsenal
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