Ivanovic headed home a pinpoint Willian free-kick in the 94th minute to provide breathing space for the Blues, who were already set to progress on away goals after a 1-1 draw at Anfield a week ago and a goalless stalemate in regulation time at Stamford Bridge.
Liverpool were left to rue missing good chances through Raheem Sterling and Philippe Coutinho in the first half, while Jordan Henderson also headed wide when unmarked in extra-time.
