Former Everton defender Marco Materazzi was booked and then sent off for twice pulling back Fernando Torres inside 30 minutes - but the hosts initially failed to take advantage.
However, with six minutes to go Dirk Kuyt fired a right-foot volley past Julio Cesar - and then captain Steven Gerrard drilled a 20-yard strike in off the post to give Liverpool a huge advantage heading into the second leg at the San Siro in three weeks time.
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