Lewandowski got the newly crowned champions off the mark in the second minute and Jamal Musiala pulled the ball back for Thomas Müller to score the second goal in the 23rd. Müller crossed for Lewandowski to score his 200th goal for Bayern with a scissors kick in the 34th, and still the home side looked for more.
Lewandowski set up Kingsley Coman for the fourth before the break, then completed his hat trick with a penalty in the 66th.
Bayern ended the game with 10 men after Tanguy Nianzou was sent after a VAR consultation for taking down Breel Embolo as the last defender in the 73rd.
It made no difference. Serge Gnabry set up Leroy Sané to complete the rout in the 85th.
Leipzig’s defeat meant it could no longer overhaul Bayern, which held a seven-point lead before the late game. Two rounds remain after this weekend.
“Of course they deserve to be German champions, after this very good season, very consistent season,” Terzić said of Bayern. “But we’re happier about the points that we got today.”
Dortmund moved into the last qualification spot for the Champions League, though Eintracht Frankfurt can reclaim the position if it beats Mainz in their derby on Sunday.
Also on Saturday, Wolfsburg consolidated its hold on third place by beating Union Berlin 3-0 at home, Hoffenheim recovered from two goals down at halftime to rout already relegated Schalke 4-2, and struggling Werder Bremen drew with Bayer Leverkusen 0-0.
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Ciarán Fahey on Twitter: https://twitter.com/cfaheyAP