The Bavarian club took the attack to Lille from the first whistle and were ahead in the fifth minute when Bastain Schweinsteiger curled a free kick past Mickael Landreau.
Lille pushed for an equaliser but were punished by Bayern on the counter attack as Franck Ribery found Pizarro and the striker calmly slotted the ball into the bottom corner to double his side's lead.
The situation got worse for the visitors just five minutes later when Arjen Robben mimicked Schweinsteiger by beating Landreau with a well placed free kick.
Pizarro completed his hat-trick before the interval by first tapping in a Phillipp Lahm cross and then heading powerfully past a helpless Landreau from the centre of the box.
Munich looked relaxed in possession after the interval but did allow Salomon Kalou to snatch a consolation goal in spectacular fashion by beating Manuel Neur with a 25-yard strike.
However, the hosts restored their five-goal lead less than 10 minutes later following another venture down the wing from Lahm that ended with a cross reaching Toni Kroos, who stroked the ball in from the edge of the box.
Lille failed to put up much more resistance in the closing stages as Munich moved to the top of the group.