Once again it was away from home. The last time they clinched the title in front of its own fans came when the club were still playing at Munich's Olympiastadion in 2000.
Sevilla would have been encouraged by the comedy of errors in Bayern's defence that led to Augsburg's goal.
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 hard circumstances following Carlo Ancelotti's departure - aims to match the treble he claimed in 2012-13.
The coach, who is going back into retirement at the end of the season, also congratulated Ancelotti for his role in the title success.
The Bavarians did not get off the best of starts as they fell behind in the 18th minute through an own goal from Niklas Sule.
But the home side was unable to maintain its furious pace, and Tolisso was left completely unmarked to head in Joshua Kimmich's cross for the equalizer after a half-hour.
The turnaround was complete six minutes later as James Rodriguez sent a fine low finish into the back of the net from close range after some good work by Kimmich and Arjen Robben.
The win took Bayern on to 72 points, 20 clear of second-placed Schalke 04 who have six matches left including Saturday evening's visit to Hamburg SV.
Robert Lewandowski, who had plundered a hat-trick in Der Klassiker, had to made do with a place on the bench as Wagner led the attack while David Alaba and Arturo Vidal both were rested.
The Colombian then ensured the title was heading to Munich, hooking the ball back into play at the far post for Robben to drill his shot inside the near post on 62 minutes. Elsewhere, Bruno Labbadia claimed his first win since taking over at VfL Wolfsburg when they beat Freiburg 2-0 away with two goals from Daniel Didavi.