Serbian defender Ivanovic scored two headed goals ? his first for the club ? and Didier Drogba added a third after Fernando Torres had shot Liverpool ahead.
Next Tuesday’s second leg at Stamford Bridge may not be a mere formality just yet, but Liverpool will need an exceptional performance to stay in the competition.
Liverpool 1-3 Chelsea
Liverpool: Reina, Arbeloa, Carragher, Skrtel, Aurelio (Dossena 75), Kuyt, Lucas (Babel 79), Alonso, Riera (Benayoun 67), Gerrard, Torres.
Subs Not Used: Cavalieri, Hyypia, Agger, Ngog.
Goals: Torres 6.
Chelsea: Cech, Ivanovic, Terry, Alex, Ashley Cole, Kalou, Ballack, Essien, Lampard, Malouda, Drogba (Anelka 79).
Subs Not Used: Hilario, Carvalho, Belletti, Mancienne, Mikel, Deco.
Booked: Kalou, Terry.
Goals: Ivanovic 39, 62, Drogba 67.
Ref: Claus Bo Larsen (Denmark).