The visitors deservedly took the lead only a minute after the interval when Frank Lampard scrambled his effort over the line after a great cross from Cesar Azpilicueta.
However, the West London club were wasteful in front of goal, with Kevin De Bruyne, Frank Lampard and Demba Ba all missing glorious chances to put the game beyond doubt.
And Jose Mourinho's men were made to pay when substitute Fabio Borini, who played for Chelsea as a teenager, slid home from a tight angle in the closing moments to send the game to extra time.
The fairy tale continued for the Mackems when another substitute, Ki-Sung Yueng, placed his effort past Mark Schwarzer in the 118th minute to hand Gus Poyet a shock victory.
After a tense encounter, here are six things we can take from the game after Sunderland booked their place in the semifinal.