Goals from Zlatko Junuzovic, Florian Grillitsch and Florian Kainz condemned second-placed Leipzig to their second successive league defeat.
Bayern can extend their 10-point lead when they travel to Borussia Monchengladbach on Sunday.
Borussia Dortmund closed the gap on Leipzig to three points with Friday's 1-0 win at Ingolstadt.
Hoffenheim are a point further back, and boosted their chances