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.
Gerrard, Torres and Jose Reina all returned to Liverpool's starting line-up for tonight's Champions League clash against Inter Milan - one of the most important matches of manager Rafael Benitez's reign.
The Spaniard's position has come under increasing scrutiny after Saturday's FA Cup exit to Barnsley, and the Reds boss made five changes from that losing side - the most significant being Torres' reappearance after a hamstring injury.
Left-back Fabio Aurelio and Javier Mascherano were the others to return - with goalkeeper Charles Itandje, John Arne Riise, Yossi Benayoun, Xabi Alonso and Peter Crouch all dropped to the bench.
Torres proved too much of a handful for Materazzi in the 30th minute and it cost the Italian dear.
The central defender, having already been booked, grabbed hold of the striker's shoulder as he raced past him and the referee had no hesitation in showing a second yellow card, followed by a red.
It wasn't until the 84th minute that Liverpool were in front at last thanks to Kuyt's second goal in successive matches.
Pennant's cross from the right evaded everyone and fell to the Dutchman at the far post.
He took a touch before hammering a shot into the ground which appeared to take a slight deflection of Maicon before beating Cesar.
Gerrard made it even better in the last minute when his drilled right-foot shot from 20 yards went in off the right-hand post.