The Blues appeared to be heading towards a shock exit after falling two goals behind, but the introduction of Cole Palmer, Morgan Rogers, Pedro Neto and Reece James at half-time completely transformed the contest.
• Chelsea: Cole Palmer 53' (pen), 55', Pedro Neto 60', Danny Welbeck 65', Valentín Barco 80', Danny Welbeck 90+4'
• Leeds United: Tarik Muharemović 23', Brenden Aaronson 48', Dominic Calvert-Lewin 75'
Chelsea started brightly but struggled to maintain their early momentum as Leeds gradually took control of the first half. The visitors threatened repeatedly from set pieces before taking the lead in the 23rd minute.
Tarik Muharemović rose to meet Harry Wilson's deep corner and headed beyond Mike Penders to give Leeds a 1–0 advantage.
Chelsea's heavily rotated side struggled to respond before the interval, with Xabi Alonso deciding to make four changes at half-time. Palmer, Rogers, Neto and James were introduced as Chelsea searched for a way back into the game.
The changes initially appeared to make little difference when Leeds doubled their advantage just three minutes into the second half. Brenden Aaronson finished after good work involving Ethan Ampadu and Lukas Nmecha to put Leeds 2–0 ahead.
Then the game changed dramatically.
Chelsea were awarded a penalty in the 53rd minute after Dan James was judged to have fouled Pep Chavarría inside the area. Palmer calmly converted from the spot to give the hosts hope.
Just two minutes later, the England international struck again, finishing after an inventive flick from Rogers to level the score at 2–2.
Chelsea completed their remarkable turnaround in the 60th minute when Pedro Neto finished from another Rogers-created opportunity to put the Blues ahead for the first time.
Rogers continued to torment the Leeds defence, supplying another assist for Danny Welbeck, who made it 4–2 in the 65th minute.
Leeds refused to surrender and reduced the deficit through substitute Dominic Calvert-Lewin in the 75th minute, setting up a tense final quarter of an hour.
Chelsea, however, restored their two-goal cushion five minutes later when Valentín Barco fired home from the right side of the attack, with Rogers again involved in the build-up.
Welbeck then completed the rout in stoppage time, heading home Chelsea's sixth goal to cap an extraordinary transformation from 2–0 down to a 6–3 victory.
The result sends Chelsea into the next round of the Carabao Cup and provides Alonso with another demonstration of the attacking depth available to him.
The victory was particularly impressive given that Chelsea had made nine changes from the side that started Sunday's 2–1 Premier League defeat to Arsenal. Sixteen-year-old Reggie Watson also made his senior debut from the start, becoming one of the youngest players to represent the club.
For Leeds, the defeat was a painful collapse after they had looked firmly in control for much of the opening hour. Chelsea's second-half response, led by Palmer and Rogers, ultimately proved too much for Daniel Farke's side.