In what was a pulsating cup tie at Stamford Bridge on Tuesday night, Chelsea were lucky to keep their full complement of players on the pitch after Diego Costa appeared to stamp on Emre Can in the first half.
However, referee Michael Oliver was unmoved just as he was when Jose Mourinho’s side thought they should have had a penalty after Martin Skrtel’s challenge on Costa midway through the first-half.
In what was an end-to-end semi-final second-leg contest, Liverpool had the better chances of the first period but Alberto Moreno and Philippe Coutinho were both denied by excellent saves from Thibaut Courtois.
After the break, Costa was once again involved in controversy as he appeared to stamp again, this time on Skrtel, but once again there was no action taken against the Spain striker.
He could have made his luck count when bearing down on goal midway through the second half, but with just the goalkeeper to beat, Simon Mignolet made a vital last-ditch tackle.
Both sides had their chances to win it at the end of normal time but in what was a tale of two Belgian goalkeepers, Courtois and Mignolet were in inspired form as the scores stayed locked at 0-0.
However, it did not take long for the deadlock to be broken in extra-time as Ivanovic rose highest to head home Willian’s free-kick and book his side’s place in the Capital One Cup final against Tottenham or Sheffield United at Wembley on Sunday, March 1.
Chelsea boss Mourinho, who made nine changes to his side following the shock home defeat by Bradford, spent much of the night fuming, but it was Reds boss Brendan Rodgers who had reason to feel most aggrieved early on as Costa should have been sent off for stamping on Can’s ankle.
Minutes later, Kurt Zouma, in the Chelsea side in place of Gary Cahill, misjudged a long ball and Raheem Sterling looked to take advantage – but the Frenchman used his pace well to recover and stop the England forward in his tracks.
Costa should then have had a penalty when tripped by Skrtel, but referee Michael Oliver waved away appeals, much to the astonishment and anger of Mourinho.
Twice Liverpool spurned chances to take the lead as Courtois saved well from Moreno and then Coutinho, while Mignolet twice denied Costa at the other end.
Mourinho raged at Oliver at half-time and his mood would not have improved when Cesc Fabregas was forced to leave the field minutes after the break to be replaced by Ramires, especially with the visit of Manchester City looming on Saturday.
Costa was once again in the thick of the action as he appeared to issue another stamp, with Skrtel the recipient this time, but the Blues striker avoided any punishment.
He could have made Liverpool pay midway through the second half but Mignolet was on hand to make a vital last-ditch tackle with Costa bearing down on goal. Seconds later, Sterling was the one trying to latch onto a misplaced pass but this time it was Courtois who was quick off his line, saving at the feet of the striker.
There was more Mourinho anger when Jordan Henderson avoided a second booking for handball late on in the game and his displeasure with the officials continued into extra-time as he missed Ivanovic’s header while talking to fourth official Phil Dowd.
With Manchester City the visitors to Stamford Bridge in the Premier League on Saturday, the additional half hour was less than welcome, but they had the final word as Ivanovic headed home Willian’s free-kick from close range to book their place at Wembley.
They now await the winner of Sheffield United’s clash with Tottenham on Wednesday night, with the first silverware of the season up for grabs on March 1.
Watch the second Capital One Cup semi-final second-leg tie between Sheffield United and Tottenham live on Sky Sports 1 HD on Wednesday night from 7.30pm, and the Premier League clash between Chelsea and Manchester City live on Sky Sports 1 HD on Saturday night from 4.45pm.