After being presented with the trophy on Saturday, Bayern captain Manuel Neuer gave it to Muller to hoist towards the Munich sky and start the confetti-filled celebrations.
There was another outpouring of emotion when Harry Kane got his chance to lift the "salad bowl" as it was the England captain's first team trophy after a career of near-misses.
Bayern won the title last weekend and Michael Olise made sure of this win by scoring one goal and setting up the other for Kane's league-leading 25th of the season to get the party underway in Munich.
At the other end of the table, Bochum and Holstein Kiel were both relegated while Leipzig's hopes of Champions League qualification were over after they could only draw 0-0 at Werder Bremen.
Last-placed Bochum lost at home to Mainz 4-1, and Kiel lost at home 2-1 to Freiburg, who consolidated fourth place and look well-placed for Champions League qualification.
Leipzig's scoreless draw in Bremen left them four points behind Freiburg with one round remaining, meaning they can no longer qualify for Europe's lucrative premier competition.
Neither Bochum nor Kiel have any possibility of catching third-from-bottom Heidenheim.
That followed Heidenheim's 3-0 win at Union Berlin, which ensures they at least have a relegation play-off place.
With one game left, Bochum have 22 points, Kiel 25, and Heidenheim 29 – just two behind St. Pauli, who have two matches remaining, the first being against third-placed Eintracht Frankfurt on Sunday.
Bochum needed to avoid defeat and hope for a favour from Union against Heidenheim at the same time. But Mainz were 3-0 up before Bochum scored.
Kiel were promoted for the first time only last season but coach Marcel Rapp's team have quickly returned to the second division.
Kiel scored first but Johan Manzambi equalized before the break and Lucas Holer headed Freiburg toward the Champions League.
Freiburg moved four points clear of Borussia Dortmund, who visit Bayer Leverkusen on Sunday for Xabi Alonso's last home game as Leverkusen coach.
Victory for Leverkusen would send Freiburg to the Champions League.
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