Bayern's probable Champions League final opponents Borussia Dortmund beat Fortuna Dusseldorf 2-1 with the help of a stunning Nuri Sahin goal.
Werder Bremen were sucked closer to the danger zone after losing 1-0 to a controversial penalty at third-placed Bayer Leverkusen, leaving them only two points clear of the relegation play-off place after Augsburg beat VfB Stuttgart 3-0.
Augsburg's win meant bottom club Greuther Furth, making their Bundesliga debut this season, were relegated. Furth lost 3-2 at home to Hannover 96 on Friday.
Xherdan Shaqiri's first-half free-kick put treble-chasing Bayern on 84 points, three more than the previous record set by Dortmund last season, with three games to play.
The Bavarians made 10 changes from the team that started Tuesday's 4-0 Champions League semi-final first leg win over Barcelona and clocked up their 27th victory in 31 league games, improving their goal difference to 76.
It was Bayern's 14th successive league win although the single goal was something of a letdown for a team that had blasted 20 in their last four matches in all competitions.
"What [coach] Christian Streich has achieved in Freiburg is sensational," said Bayern coach Jupp Heynckes. "A lot of things have come together there over a period of years.
"It was a hard job of work today but credit to the lads. We were very smart and very professional."
