The 72-year-old Heynckes, in his fourth stint at the club, took over last week from the sacked Carlo Ancelotti with the club having failed to win any of their last three matches in all competitions.
Heynckes, who led Bayern to the 2013 treble, could have not picked more appropriate opponents, with Freiburg having never won in Munich and having lost 13 of their 15 previous league matches in the Bavarian capital before Saturday.
The hosts needed only eight minutes to take the lead with Freiburg's Julian Schuster's second own goal in consecutive matches following a flowing passing move from the hosts.
Kingsley Coman's diving header after Arjen Robben had his effort palmed away in the 42nd minute gave them a two-goal cushion but instead of wasting it as they had done in their last two league games where they ended up drawing 2-2, Bayern cruised to victory. Thiago Alcantara capped an outstanding personal performance with a goal, his powerful low shot beating keeper Alexander Schwolow just past the hour before forward Robert Lewandowski pounced on a defensive error to take his goal tally to nine. Bayern completed the rout in stoppage time with Joshua Kimmich scoring on the break.
Hoffenheim, in third place, twice led against Augsburg but conceded a last-gasp goal for a 2-2 draw that left them on 15 points.