The South Korean midfielder, on loan from Swansea City, netted in extra-time as the Black Cats came from behind to beat the Blues at the Stadium of Light, allowing them to move into the semi-final.
Just as it seemed the Blues were headed for victory, Fabio Borini came off the bench to rifle home an 88th-minute equaliser, sending the contest into 15 minutes each way of added time.
Sunderland worked their socks off during that phase and it paid dividends as Ki, who earlier had a goal-bound header brilliantly denied by Mark Schwarzer, was able to fire past the left hand of the veteran in the 118th minute.
Capital One Cup - quarter-final
For breaking stories and all the great banter like us on Facebook: facebook.com/tribalfootball