The visitors’ defence was highly culpable as Shinji Okazaki ended a 13-game goal drought with two first-half goals for the Premier League champions, but two of Antonio Conte’s back four were able to make amends either side of the interval.
Captain Gary Cahill headed home a Fabregas corner in first-half stoppage time before Cesar Azpilicueta – who tried in vain to hack both Okazaki goals off the line – elevated a pulsating match further with a spectacular long-range volley in the 49th minute.
Leicester were forced to play the additional half-hour with 10 men after Marcin Wasilewski struck substitute Diego Costa with a forearm and Chelsea made merry against reduced numbers as Fabregas struck twice inside the opening four minutes of extra-time.
The match took place following conflicting reports of Chelsea owner Roman Abramovich’s displeasure regarding last Friday’s 2-1 loss to Liverpool, meaning Conte’s men turned in a timely showing of character and class.
Marcos Alonso was selected for his Chelsea debut as both managers made seven changes and it was the reshuffled visitors who settled quickest.
Pedro had an early goal chalked off for a marginal offside and Wasilewski breathed easily when referee Robert Madley did not punish him for handling inside the box.
There was a similar sense of relief for Cahill when his pass was intercepted by Okazaki and his subsequent collision with Ahmed Musa in the penalty area went unpunished.
Nevertheless, Chelsea remained some way below Conte’s famously exacting defensive standards and fell behind thanks to some dismal defending after 17 minutes.
Azpilicueta chested Musa’s right-wing cross back across his own six-yard box and could not rescue the situation after Okazaki reacted quicker than a lumbering Asmir Begovic to head the opener.
Michy Batshuayi should have done better when he nodded Pedro’s delivery wide at the back post and Chelsea’s task became steeper 11 minutes before half-time.
Okazaki took Andy King’s lofted pass impressively on his chest, but was ably assisted by a ball-watching David Luiz as he scuffed a shot into the turf, over Begovic and in.
A chastening half for Chelsea’s defence ended on a high – Cahill heading over the line, with Luiz charging into Danny Drinkwater’s clearance to make sure.
The equaliser arrived four minutes after the restart and in spectacular fashion, as Fabregas’ cross was only partially cleared and a sweetly hit volley from Azpilicueta flew into the top corner from 25 yards.
Batshuayi tried to pick out the same part of Ron-Robert Zieler’s goal midway through the second half, only for the Germany international to produce a superb flying save.
With his team increasingly camped close to his penalty area, a long Zieler clearance sent Musa darting through at the other end, with Begovic turning his chip unconvincingly behind before King missed a glorious headed chance from the resulting corner.
A raking pass from Luiz saw Costa force a double save from Zieler before Wasilewski – already on a booking – foolishly ensured his early exit.
Costa rifled against the side-netting in stoppage time but linked smoothly with fellow replacement Eden Hazard, who ruthlessly exposed a flagging Leicester by backheeling for Fabregas to score wonderfully in the 92nd minute.
A poor Zieler punch allowed Fabregas to smash a second to seal the tie and quell talk of early cracks appearing under Conte.