Pizarro, who grabbed a starting spot after Bayern's top scorer Mario Mandzukic was ruled out with a cold, used his chance to display all the skills that have made him the Bundesliga's top foreign scorer of all time and scoring three times in 15 minutes.
"It has been some time that I have scored three goals in one half," the 34-year-old told reporters with a big smile. "I am very happy to have scored.
"We played very well from the start and the early goal was important," he added in reference to Bastian Schweinsteiger's fifth minute goal from a curled free-kick.
"Then the goals started coming. It was just fun to play out there tonight. I hope it continues like that."
Pizarro returned to Bayern this season after spells as Chelsea and Werder Bremen as an attacking option. Mandzukic, however, had been first choice this season with Mario Gomez still out since surgery in August.
The tall Peruvian, however, who also scored twice in Bayern's German Cup second round last week, did not let this chance slip by.
He opened his account in the 18th minute with a low shot from 16 metres, adding another 10 minutes later with a close-range flick worthy of a world class centre-forward.
Pizarro grabbed his hat-trick in the 33rd, rising high to meet another Philipp Lahm cross and drill in his header.
The forward, who played for Bayern between 2001-07, even had time for a sideline dance with Brazilians Dante and Rafinha after his first goal.
"We had organised it before and said that if I score I will dance a Brazilian dance," Pizarro said.
