It took the Bavarians 69 minutes to get going at the Allianz Arena but Thomas Muller, Xherdan Shaqiri and Luiz Gustavo then struck to give them another win and take them on to a record 88 points for the season.
Shortly after the final whistle, Bayern picked up their first trophy in three years before setting off on a parade from the stadium to the city centre, where 20,000 fans were expected to greet them on the balcony of the City Hall.
Stuttgart ruined Schalke's potential Champions League qualification party on the day the hosts' coach Jens Keller extended his contract with a 2-1 win at the Arena AufSchalke.
Vedad Ibisevic's double helped the Swabians take all three points and leave Schalke needing to avoid defeat on the final day of the season in a Champions League decider against Freiburg to achieve their aim for the season.
An own goal from Georg Niedermeier in the last minute was too little too late for the Royal Blues, who hold on to fourth place by a single point.
Freiburg came from behind to beat relegated Greuther Furth 2-1.
Werder Bremen celebrated securing their place in the Bundesliga next season with a 1-1 draw against Eintracht Frankfurt.
Kevin de Bruyne gave the northern club the lead midway through the first half before Srdjan Lakic levelled for the Eagles.
But with Augsburg and Fortuna Dusseldorf both losing, the point was all Bremen needed to move four points clear of the relegation zone and ensure top-flight football will be played at the Weser Stadion again next season.
Dusseldorf threw away a half-time lead in their 2-1 defeat against Nurnberg.
Hamburg pushed Hoffenheim closer to the 2. Bundesliga with a convincing win which keeps their own hopes of European football next season alive going into the final round of matches next weekend.
Son Heung-min, Dennis Aogo, Petr Jiracek and Arjoms Rudnevs were all on target for Thorsten Fink's men with Kevin Volland's goal worthless for a Hoffenheim side who remain two points adrift of safety and now needing something special to avoid relegation.
Hannover's lingering hopes of qualifying for the Europa League next season were ended in emphatic fashion by Bayer Leverkusen at the BayArena.
Two goals from Jens Hegeler and a header from the Bundesliga's top goalscorer Stefan Kiessling earned Leverkusen a comfortable 3-1 win with Artur Sobiech grabbing a consolation for the visitors.
Wolfsburg and Borussia Dortmund shared six goals in a pulsating encounter at the VW-Arena.
Dortmund went ahead through Sven Bender in the fifth minute, but three goals in the space of 12 minutes turned the game on its head.
A brace from Ivan Perisic was followed by goal from Naldo as the Wolves took control of the game and it looked like they were going to get a prestigious win until Marco Reus scored two late goals to earn Dortmund a share of the spoils.
Twenty-year-old striker Branimir Hrgota hit a hat-trick to open his account for Borussia Monchengladbach in style as they earned an entertaining Bundesliga win at Mainz.
The Sweden Under-21 international had failed to score in his previous 11 games for Gladbach, but ended the drought with a penalty just before half-time to cancel out Shawn Parker's opener.
Hrgota put the visitors in front in the 59th minute and, after Mike Hanke had added a third, completed his treble 10 minutes from time.
Andreas Ivanschitz got Mainz's second with an injury-time penalty, but it could not stop Gladbach keeping their, admittedly very slim, European hopes just about alive.