Ex-Peru international Pizarro cannily stroked a set-piece through the home side's wall in the sixth minute of stoppage-time.
At 40 years, four months and 13 days, the veteran attacker claimed the record previously held by ex-Bremen midfielder Mirko Votava, who was just over a month younger when he netted against Stuttgart in August 1996.
The goal was Pizarro's third in 17 league appearances this term and kept Werder within a point of ninth-placed Hertha.
"I'm very happy, very proud about [becoming the oldest scorer in Bundesliga history]," Pizarro said.
"We had one opportunity at the end, and we scored. One point is very important."
Pizarro has had five separate spells with Werder, first joining them Allianza Lima in 1999.
He has also spent time at Chelsea and Bayern Munich in a lengthy career at the top level.