Jose Mourinho's side looked in control when Frank Lampard bundled Cesar Azpilicueta's low cross from the right over the line in the first minute of the second half despite a last-gasp tackle from Lee Cattermole.
Samuel Eto'o had a great chance to double Chelsea's advantage when one-on-one with Vito Mannone after a Craig Gardner mistake, but the Cameroon striker stroked his shot just wide.
Sunderland substitute Fabio Borini made Chelsea pay for their profligacy when he levelled with a sharp finish from a tight angle two minutes from the end, after good build-up play by Jozy Altidore.
And with penalties looming at the end of extra-time, Ki fired Sunderland into the semi-finals with a fine finish two minutes before the end, as he dropped his shoulder to cut inside Ashley Cole then beat Chelsea goalkeeper Mark Schwarzer with a low shot.
37' - Schuerrle cuts inside Cattermole but drags his shot wide of goal.
46' - GOAL: Lampard bundles Azpilicueta's low cross from the right over the line despite the pressure from Cattermole.
55' - Lampard nicks the ball off Larsson, and Mannone does well to save from De Bruyne.
69' - Cattermole's effort from the edge of the box is saved by Schwarzer.
88' - GOAL: Borini scores from the angle after Schwarzer saves from Altidore.
97' - Ba dives to try and divert De Bruyne's cross past Mannone at the near post, but the Italian makes the save.
112' - Larsson's free-kick is saved by Schwarzer, who then is up quickly to deny Altidore with the follow-up.
117' - GOAL: Borini finds Ki in the box, and the Korean drops the shoulder and beats Schwarzer at the near post.
Frank Lampard has scored nine goals in 12 appearances against Sunderland.
Chelsea had not conceded a goal in the Capital One Cup this season until tonight.
Chelsea manager Jose Mourinho has only lost twice in the League Cup through his career.
Can Sunderland use this result as a springboard to Premier League safety? Manager Gus Poyet said before the match that there is "no better boost for a team than beating Chelsea" - can they now translate the confidence gleaned from this victory to their battle against relegation?
MAN OF THE MATCH:
Lee Cattermole (Sunderland): He might not be the most technically proficient footballer, but his work-rate and tigerish tackling helped Sunderland win the midfield battle.
SUNDERLAND: Mannone 7, Celustka 7, Dossena 7, O'Shea 7, Brown 8, Cattermole 9, Larsson 7, Gardner 7, Johnson 7, Giaccherini 8, Altidore 6. Subs: Ki 8, Borini.
CHELSEA: Schwarzer 7; Azpilicueta 7, Cahill 7, D Luiz 7, Cole 6, Mikel 6, Lampard 7, De Bruyne 7, Willian 7, Schurrle 7, Eto’o 5. Subs:Essien 6, Hazard 6, Ba 6.
THE MATCH IN A TWEET