Back in charge for the fourth time, Heynckes encountered few troubles in guiding the champions back to winning ways as two first-half goals effectively put the result beyond doubt.
Sven Ulreich proved his value as Manuel Neuer's injury replacement with an important early save from Ryan Kent, with the Bavarian giants taking advantage through Julian Schuster's own goal.
The Freiburg captain became the first player in over 26 years to find his own net in successive Bundesliga matches and the error was compounded when Coman struck prior to the interval.
Thiago Alcantara wrapped up three points just after the hour to momentarily reduce Borussia Dortmund's lead at the top to two points.
Robert Lewandowski added a fourth and Joshua Kimmich put the icing on the cake with a sumptuous fifth as Heynckes' reign started as his last finished in 2013 - in style.
Bayern's party was almost spoiled inside six minutes as Liverpool loanee Kent was played through on goal, but Ulreich spread himself well to save with his feet.
Kent's wasted chance proved costly as the hosts went ahead just two minutes later. Coman found Alaba on the overlap and the Austrian's low cross was bundled in for an own goal by Schuster.
Javi Martinez then directed a header wide from Joshua Kimmich's corner as Heynckes' men stamped their authority on possession and territory.
Freiburg were not without their chances on the counter-attack, though, with Kent seeing another attempt blocked, before a fast-arriving Mike Frantz headed Christian Gunter's teasing cross narrowly around the post.
And the visitors came to rue their misfortune once more when Alexander Schwolow's initial save from Arjen Robben fell kindly for Coman to head in a second shortly before the break.
Christian Streich's side did well to steady over the opening 15 minutes of the second half, until Bayern had appeals for a penalty denied by the Video Assistant Referee.
Instead, it was left to midfielder Thiago to make it 3-0 just beyond the hour with a fizzing low finish into the bottom right corner from outside the area.
Bayern did suffer a setback when Martinez was forced off clutching his shoulder, but they soon put that to one side as Thomas Muller won possession on the right and found Lewandowski for a simple finish.
Schwolow then saved skipper Schuster from heading in a second own goal of the match, although that did little to brighten a difficult afternoon for last season's seventh-placed side.
And there was still time for the home side to add fifth as Coman turned provider, pulling a clever pass across the face for Kimmich to delightfully backheel in at point-blank range.
Key Opta Facts:
- Jupp Heynckes became the third oldest coach in Bundesliga history (72 years, 158 days). Only Fred Schulz in 1978 for Werder Bremen (74 years, 67 days) and Otto Rehhagel in 2012 for Hertha Berlin (73 years, 194 days) have been older.
- Heynckes won his first competitive match as Bayern coach in each of his four stints.
- Freiburg lost their 14th match in a row at Bayern Munich in the Bundesliga. Only one team in history has lost more away matches in a row at one other team: Wolfsburg (15 at Bayern).
- Joshua Kimmich has had a hand in seven Bayern goals in competitive matches this season (two goals, five assists). He is the player with the second most goal involvements for Bayern in this season (after Lewandowski who scored 13 goals with no assist).
- Only one Bayern coach celebrated a higher win in the first competitive match of his stint: Udo Lattek in March 1970 (6-0 vs. Aachen).