The win also moved them close to a 35th national title because their only challengers for the trophy, Borussia Dortmund, lost earlier on Saturday.
League leaders Bayern equalled their 101 goals from the 1971/72 season through Jamal Musiala's header in the ninth minute and bettered the mark to 102 when midfielder Leon Goretzka, who will leave in summer, fired home for 2-0 in the 53rd minute.
"I didn't know it (was the record). I had others explain it to me. It was a nice goal," Goretzka told Sky TV.
Coach Vincent Kompany said: "Leon always believes in his moments. He is a great example for the others. The record stood so long. I like it that we have the record."
Michael Olise got the third a minute later before Nicolas Jackson in 65th and Raphael Guerreiro in the 88th wrapped up matters and boosted morale for their big Champions League quarter-final against Real Madrid on Wednesday, having won the first leg in Spain 2-1.
Bayern have scored 45 goals more than the second best team, Dortmund, who have 60. The final tally is expected to be even higher as there are five more matchdays.
Bayern moved 12 points clear of Dortmund who lost 1-0 at home against top four candidates Bayer Leverkusen from Robert Andrich's 42nd-minute winner.
They have a first chance to clinch the title next weekend if they get one point more than Dortmund. Bayern host VfB Stuttgart and Dortmund are at Hoffenheim.
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