Neither side could be separated after 90 minutes in the semi-final second leg before Ivanovic leapt highest to meet Willian's free-kick in the 94th minute to wrap up a 2-1 aggregate win and a trip to Wembley in March.
However, the match was noteworthy for a series of flashpoints involving Diego Costa, including a stamping incident in each half on Emre Can and Martin Skrtel.
The Spain international was at the heart of more contention when he was denied a penalty by referee Michael Oliver after going to ground under a challenge from Skrtel just after the 20 minute mark.
Chelsea goalkeeper Thibaut Courtois also made two brilliant one-on-one saves from Alberto Moreno and Philippe Coutinho in the first half that ultimately proved crucial.
Victory over Liverpool represents an ideal response for Chelsea after Saturday's 4-2 FA Cup defeat to League One side Bradford City that left manager Jose Mourinho fuming.
The Portuguese - who was involved in a touchline exchange with Brendan Rodgers - now has his sights set on a third League Cup title, the first of which came against Liverpool in 2005 and was his first trophy in English football during his first stint at the club.
Chelsea had shouts for a penalty waved away in an end-to-end opening when Willian's low shot struck the arm of the sliding Lucas Leiva.
Can and Costa were then involved a brief altercation after the latter was lucky to escape punishment for seemingly stamping on the Liverpool midfielder's shin.
Costa was in the spotlight again in the 22nd minute as he went to ground when Skrtel looked to have stood on his foot, but referee Oliver was uninterested.
At the other end, Steven Gerrard's superb pass picked out the run of Moreno on the left of the area, with the full-back's subsequent shot well parried by Courtois, before the Belgium international saved Coutinho's drive with his foot after the Brazilian waltzed through the Chelsea defence.
The home side were dealt a blow when Cesc Fabregas had to be replaced following an accidental collision with team-mate John Terry shortly after the restart.
Tempers then threatened to boil over when Costa appeared to tread on Skrtel, leading to an angry coming together between the two players.
Eden Hazard, scorer of Chelsea's goal in the first leg, gave a timely reminder of his brilliance with a mazy run that led to him fizzing a shot just wide from 20 yards, before Simon Mignolet made a terrific block with his feet to keep out Costa's deflected half-volley.
Liverpool were then fortunate not to be reduced to 10 men in the 67th minute when Jordan Henderson avoided a second yellow card for a deliberate hand ball, before Chelsea's Filipe Luis hobbled off after taking a knock.
The breakthrough finally came four minutes into extra time, as Willian's teasing free-kick was headed home emphatically by Ivanovic.
Henderson could have forced penalties when he put a free header wide from 10 yards, but ultimately Chelsea safely saw out extra time to reach their first final since Mourinho's return in June 2013.
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