The 34-year-old, in the starting lineup only because top scorer Mario Mandzukic was ill, notched the Champions League's third fastest hat-trick as Bayern recorded the biggest halftime lead in the competition's history.
Bastian Schweinsteiger and Arjen Robben scored from free kicks and Toni Kroos fired in from 16 metres in the second half as Bayern rode roughshod over Lille, who briefly cut the lead with a Salomon Kalou goal.
Bayern's win put them on nine points in the group alongside Valencia who beat BATE Borisov 4-2. BATE are on six with bottom-placed Lille having lost all four group matches.
"I had said before the game that we need to win this, draw in Valencia and win our last home game against BATE and that is the situation in the group," said Bayern coach Jupp Heynckes, who played down the big win.
"Obviously we had great plays in the first half. We also had two free kick goals which is something we trained but the opponent was not in top form tonight. I do not want to put a dampener on things but that is what it is," he told reporters.
Bayern, who have now won 16 of their last 17 home games, shot out of the blocks with Schweinsteiger curling a free-kick over the wall for the lead after five minutes and Thomas Muller squandering two golden chances.
ROBBEN BACK
With Dutchman Robben back in the team for a European match after a one-month injury layoff, and Franck Ribery in sparkling form, the hosts, who are also leading the Bundesliga by seven points with nine wins out of 10 matches, were unstoppable.
Pizarro doubled their lead with a stunning low drive after a one-two with Ribery at the edge of the box leaving the Lille defence in tatters.
They added another with a heavily deflected free kick from Robben before Pizarro flicked in his second goal from close range from captain Philipp Lahm's well-timed cutback.
"They scored with almost every attempt on goal and it is difficult to keep shine if you concede a goal every time," said Lille captain Rio Mavuba who came on as a substitute.
"We are now out of the competition. It hurts. We fought last year to be here tonight and to produce a performance that is not worthy of Lille is really disappointing."
Lille, who had never scored in Germany before and have now lost their last four fixtures against Bundesliga sides, got a bit more possession in the second half as the Bavarians eased off.
They cut the deficit with a fine Kalou shot from the edge of the box but it was back to business for Bayern with Kroos' low drive in the 66th minute after another layoff from Lahm to complete the rout.
Lille had keeper Mickael Landreau to thank for keeping the score at 6-1, repeatedly denying Robben in the final minutes from point blank range.
"That is how we have to play every game. It was of the highest quality," Robben told reporters. "But it was not gifted to us, we created it for us."
