Timo Werner struck his first Blues goal 19 minutes into the contest at Tottenham Hotspur Stadium and it looked to be enough to send them into the last eight for the 14th time in the past 20 seasons.
However, Erik Lamela, who started as a makeshift striker, drilled past debutant Edouard Mendy to give Spurs a deserved equaliser with seven minutes of normal time remaining.
The first nine penalties of the ensuing shoot-out were converted before Mason Mount clipped the outside of the left post with the 10th, allowing Spurs to progress.
Chelsea made eight changes from their Premier League draw with West Brom on Saturday, handing full debuts to Ben Chilwell and new goalkeeper Mendy, while Harry Kane dropping to the bench was one of nine alterations for Spurs from their draw with Newcastle United.
Sergio Reguilon's debut did not start according to plan, as the Tottenham left-back lost possession and was easily beaten by Cesar Azpilicueta, whose deflected low cross allowed Werner to fire low past Hugo Lloris.
35 - Since the start of last season, only Robert Lewandowski (56), Ciro Immobile (40) and Cristiano Ronaldo (40) have scored more goals than Timo Werner (35) for top five European league sides in all competitions. Blue. #TOTCHE #CarabaoCup pic.twitter.com/6pYTAGe186— OptaJoe (@OptaJoe) September 29, 2020
Mendy was also given a busy first half in English football, just managing to stop Gedson Fernandes along with Kurt Zouma and then blocking Lamela's strike with his legs.
Reguilon and Mendy came face to face early in the second half, the Spurs man's stinging strike palmed over the bar after good play from Serge Aurier.
Mourinho threw on Kane with a little over 20 minutes left as Spurs maintained their pressure, but it was Lamela who levelled, slotting low past Mendy after working space from Reguilon's cross.
Eric Dier, Tammy Abraham, Lamela, Azpilicueta, Pierre-Emile Hojbjerg, Jorginho, Lucas Moura, Emerson Palmieri and Kane all scored before Mount's crucial miss, as Spurs avenged their shoot-out defeat in the semi-finals of two seasons ago.