That decision looked to have backfired as Niklas Sule's 18th-minute own goal gave Augsburg the lead, but two goals in quick succession swung the game in Bayern's favour.
Corentin Tolisso's header restored parity after 32 minutes, and Bayern took control when James Rodriguez slotted in following excellent build-up play from Joshua Kimmich and Juan Bernat.
Augsburg failed to match their early intensity following the second-half restart - Arjen Robben extending Bayern's lead just after the hour and Sandro Wagner adding further gloss to the victory late on.
With another Bundesliga crown now wrapped up, Bayern's attention will now switch to their European and DFB-Pokal campaigns, as Heynckes - who took charge in difficult circumstances following Carlo Ancelotti's departure - aims to match the treble he claimed in 2012-13.
Determined to delay Bayern's celebrations, Augsburg looked threatening early on - Caiuby flashing a well-struck effort across the face of goal.
Philipp Max was the next to test Bayern's resolve, racing in behind the visitors' defence before hammering a powerful strike against Sven Ulreich's near post, but Augbsurg did take a deserved lead soon after.
Jerome Boateng's untimely slip enabled Sergio Cordova to pounce, and, although the winger's effort was saved by Ulreich, the ball rebounded back in off the unfortunate Sule.
Augsburg's lead was short-lived, however, as - from Bayern's first meaningful attack - Tolisso drifted into the area to head home unmarked from Kimmich's precise cross.
It took Bayern just six minutes to double their tally, Bernat's clever flick teeing up James, who made no mistake with a neat first-time finish into the bottom-left corner.
Tolisso could have had his second prior to the interval as Bayern clicked through the gears, but Marwin Hitz did well to parry the Frenchman's strike wide.
Bayern's domination continued after the interval, with Augsburg offering little going forward at the other end.
And the pressure proved too much for Augsburg in the 62nd minute as Robben, whose future at the club remains uncertain, hammered in a third after the hosts failed to clear Kimmich's cross.
Augsburg finally rallied as the game entered its final 20 minutes - Michael Gregoritsch's cross-cum-shot whistling just off target.
A fine save from Hitz denied Robben a second as Bayern looked to run riot, with Sebastian Rudy passing up a golden chance to net his first Bundesliga goal of the season.
Those misses ultimately mattered little, though, Wagner planting a powerful header into the top-right corner as Bayern celebrated their unprecedented sixth consecutive league title in style.