Bayern, who have won 28 German titles altogether, had eased up by then but there was still time for Sandro Wagner to score a fourth in the 86th minute.
Bayern were three points behind leaders Borussia Dortmund when Ancelotti left but ran away with the title under Heynckes, winning 19 out of 22 league matches under his leadership to take the title with five matches to spare.
Heynckes could yet cap a fairytale return by winning the European Cup for the sixth time in Bayern's history in the Champions League final in Kiev on May 26.
Bayern's Bavarian neighbours Augsburg, though, were out to spoil the party and took an early lead through a freaky own-goal from defender Niklas Sule after 18 minutes.
Heynckes also claimed that he "never imagined" Bayern would win the league this season when he was called upon to take over at the Allianz Arena back in October, insisting that his priority was just to steady the ship in Bavaria.
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. "Everyone delivered great work".
Bayern Munich's Arjen Robben celebrates scoring their third goal against Augsburg.
"Other teams have contacted me", Robben told Sky, having also won the Spanish and English league titles with Real Madrid and Chelsea respectively.
"The coach is responsible for the big picture, but first and foremost the players are the protagonists, they have done an outstanding job", said Heynckes. Goalkeeper Seven Ulreich made a parry but Niklas Suele deflected the rebound into the wrong goal with 18 minutes played.
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.
Wolfsburg struck a blow for its survival with a 2-0 win at Freiburg, and Borussia Moenchengladbach came from behind to beat visiting Hertha Berlin 2-1. Jonas Hector gave Cologne an early lead but Pablo de Blasis levelled five minutes into the second half, leaving the Billy Goats six points adrift of safety in 17th place.