With another Bundesliga crown now wrapped up, Bayern's attention will now switch to its European and DFB-Pokal campaigns, as Heynckes, who took charge in hard circumstances after Carlo Ancelotti's departure, aims to match the treble he claimed in 2012-2013. They beat Augsburg thanks to goals from Tolisso, James Rodriguez, Arjen Robben and Wagner.
Bayern have won the Bundesliga title a total of 28 times.
Bayern Munich were crowned Bundesliga champions for the sixth consecutive season on Saturday, with five games still left to play.
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They could have matched Bayern's fastest championship win - under Pep Guardiola in 2014 - but a slip-up against RB Leipzig meant they had to postpone the celebrations.
It was Robben's seventh Bundesliga crown since joining Bayern in 2009, but with his contract expiring in June, he could yet leave at the end of the campaign.
Heynckes wasted little time delivering in his fourth coaching stint at the club.
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Sevilla would have been encouraged by the comedy of errors in Bayern's defence that led to Augsburg's goal.
Sergio Cordova's shot was saved by Sven Ulreich, but bounced up into the face of Niklas Sule and rolled into the empty net, to make it 1-0. But Tolisso headed in Joshua Kimmich's cross and Rodriguez then smashed home from close range.
Wagner, playing in place of the rested Robert Lewandowski, rounded off the scoring late.
The 72-year-old, who retired after that treble success, returned at the request of Bayern bosses and good friends Uli Hoeness and Karl-Heinz Rummenigge after Italian Ancelotti departed with the team in dire need of consistency.
Hamburg suffered an early setback when Naldo appeared to score with his hand, but goals from Filip Kostic and Lewis Holby put the home side ahead before Guido Burgstaller's equalizer for Schalke.
An early goal by Cologne's Germany defender Jonas Hector was cancelled out as Pablo De Blasis headed an equaliser for Mainz five minutes into the second half.