After a 1-1 draw in the first leg, Ivanovic rose to meet Willian's free kick in the 94th minute at Stamford Bridge to secure Chelsea's progress.
"This is a game where we showed the real character of the team and we are happy, very happy," Ivanovic said.
The Premier League leaders were fortunate to complete the heated and compelling game with 11 men after Diego Costa avoided punishment for stamping on Liverpool duo Emre Can and Martin Skrtel. With Costa risking a retrospective ban, Chelsea manager Jose Mourinho defended his striker and blamed the media.
"What you call stamps and Sky (television) calls crimes, I have to say absolutely (were) accidental," Mourinho told reporters.
By denying Brendan Rodgers a first final as Liverpool manager, Mourinho can now prepare for the first since returning to Chelsea in 2013.
Chelsea, which won the competition in 2005 and 2007 under Mourinho, will discover its opponent for the March 1 final at Wembley Stadium on Wednesday. Tottenham leads Sheffield United 1-0 heading to Bramall Lane.
If there was any doubting the significance of England's second-tier knockout competition it came with the teamsheet. Unlike on Saturday when a weakened Chelsea was humiliated 4-2 here by third-tier Bradford, Mourinho was taking this trophy more seriously.
Chelsea was back at full strength, with top-scorer Costa restored to the line-up. The Spain striker made his mark early on, by leaving a mark on Can's right ankle. The stamp came in front of the benches and fourth official Phil Dowd, but Costa avoided even a yellow card.
"He could easily hurdle over the young player and he directs his studs right on to his ankle, which could've been nasty," Rodgers said.
Costa was the aggrieved player in the 22nd minute when he was tripped by Skrtel and referee Michael Oliver dismissed the penalty appeal.
"It's so clear, so clear, and that is difficult to accept," said Mourinho, who raged at the time on the touchline as the game became increasingly fiery.
It was Mourinho's goalkeeper, Thibaut Courtois, who preserved parity. The sprawling Belgian saved from Alberto Moreno and used his outstretched left leg to deny Philippe Coutinho.
Liverpool was exhibiting the attacking verve that was the hallmark of last season's run to second in the Premier League, but had been lacking in the opening months of this season. The visitors, however, could find no way past Courtois.
The second half witnessed another flare-up involving Costa, which Oliver seemed to miss. After Skrtel's sliding tackle, Costa stepped on the defender's left boot.
"There's no need to do it. That's the sad thing of it," Rodgers said. "He's a top-class player and he's clever enough that the officials don't see it."
Costa then used his boot for shooting not stamping, but a scrappy shot was blocked by goalkeeper Simon Mignolet's left leg.
Mignolet, who was dropped in December before regaining his place after Brad Jones was injured, then tackled Costa as the striker tried to round him.
In the search for a winner, Rodgers brought on misfiring striker Mario Balotelli for Lazar Markovic. But the Italian's main contribution was allowing Ivanovic to evade him to head in the winner. Away goals only count after 120 minutes, but Ivanovic's third goal of the season ensured Chelsea is back in the League Cup final after a six-year absence.
There was time for one last flare-up, though. Both Liverpool captain Steven Gerrard and Costa were booked after tangling. For Gerrard, defeat reduces his chances of ending his Liverpool career in May with a trophy.
"For us to be successful, it's got to hurt at times as well," Rodgers said.