An Ivanovic header in the fourth minute of extra-time proved the difference as Chelsea responded from the humiliating FA Cup defeat to League One Bradford to advance to a first final of Jose Mourinho's second spell as boss.
A 1-1 first-leg draw at Anfield meant it was all down to the Stamford Bridge clash and the 1-0 victory for Mourinho means he has now won four of his five contests with Brendan Rodgers, once his protege and now a bitter rival.
The managers confronted each other on the touchline as a tempestuous contest featuring nine bookings spilled into the technical area.
A comical moment followed as Liverpool assistant boss Colin Pascoe offered the Portuguese his glasses
Mourinho was not amused.
The Blues boss spent much of the night fuming, but it was Rodgers who had reason to feel most aggrieved early on as Diego Costa should have been sent off for stamping on Emre Can's ankle.
Costa should then have had a penalty when tripped by Martin 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 Thibaut Courtois saved well from Alberto Moreno and then Philippe Coutinho, while Simon Mignolet twice denied Costa at the other end.
Mourinho raged at Oliver when Jordan Henderson avoided a second booking for handball and his displeasure with the officials continued into extra-time as he missed Ivanovic's header while talking to fourth official Phil Dowd.
With Frank Lampard's Manchester City visiting Stamford Bridge in the Premier League on Saturday, the additional half hour was less than welcome, but Chelsea showed a grit and determination lacking against Bradford to prevail.
Source : PA