Ivanovic didn't play after arriving from Lokomotiv Moscow in an $18 million transfer from Lokomotiv Moscow -- the biggest in Russian history -- and had played only one Champions League game before Wednesday's encounter at Anfield.
Chelsea manager Guus Hiddink started Ivanovic in place of the injured Jose Bosingwa at right back.
"He is a very determined guy and when you are signed by Chelsea and do not play frequently, it is not easy," said Hiddink. "But he kept training with a very good mentality and although it is not his natural position, he has done well at right back. Normally, he plays in central defense. Even if you can't see a big prospect for yourself, you have to go on and at a big club it pays off. It is good to see this mentality."
Striker Fernando Torres gave Liverpool the lead at Anfield after only six minutes, but Chelsea evened the score six minutes before halftime with a header off Florent Malouda's corner.
Ivanovic added a second goal -- this time off a Frank Lampard corner -- to put Chelsea ahead after 62 minutes, and Didier Drogba put the game away with a goal off Malouda's cross five minutes later.
April 8 in Liverpool
Liverpool 1 Chelsea 3. Goals: Fernando Torres 6; Ivanovic 39, 62, Drogba 67.
Liverpool -- Reina, Arbeloa, Skrtel, Carragher, Fabio Aurelio (Dossena 75), Xabi Alonso, Lucas (Babel 79), Kuyt, Gerrard, Riera (Benayoun 68), Fernando Torres.
Chelsea -- Cech, Ivanovic, Alex, Terry, Cole, Ballack, Essien, Lampard, Kalou, Drogba (Anelka 80), Malouda.
Referee: Claus Bo Larsen (Denmark)