The victory moved second-placed Bayern, who take on Celtic in the Champions League next week, up to 17 points, two behind Dortmund who suffered their first home loss in 41 Bundesliga matches, 3-2 to RB Leipzig.
The 72-year-old Heynckes, in his fourth stint at the club, took over last week from the sacked Carlo Ancelotti after Bayern failed to win their last three matches in all competitions.
Heynckes, who led Bayern to the 2013 treble, could have not picked better opponents, with Freiburg having never won in Munich and having lost 13 of their 15 previous league matches in the Bavarian capital.
“It was very important to have a good start,” the coach told reporters. “This gives a lot of support and self confidence and security.
“In our current position we should not overestimate the 5-0 victory but it was positive that the team kept wanting to score again after the 2-0. It was a positive start but we still have a lot of work in front of us.”
The hosts needed only eight minutes to take the lead with Julian Schuster’s second own goal in consecutive matches following a flowing passing move from the hosts.
Kingsley Coman’s diving header 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 performance with a goal on the hour before 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.
Champions League clubs Dortmund and Leipzig both had a player sent off in the second half in an entertaining match with the visitors in control throughout.
Bundesliga top scorer Pierre-Emerick Aubameyang struck twice but Dortmund conceded three goals, one more than the total in the seven previous league matches, to end their unbeaten home run.
Hoffenheim, in third place, twice led against Augsburg but conceded a last-gasp goal to earn a 2-2 draw that left them on 15 points.
Schalke got their first win in four matches when they stunned hosts Hertha Berlin 2-0 to climb up to fifth on 13, three ahead of Mainz 05 who beat Hamburg SV 3-2.
RESULTS
* Bayern Munich 5 (Schuster 8-og, Coman 42, Thiago 63, Lewandowski 75, Kimmich 90+3) Freiburg 0
* Hoffenheim 2 (Huebner 52, Uth 85) Augsburg 2 (Gregoritsch 75, Vogt 89-og)
* Hertha Berlin 0 Schalke 2 (Goretzka 54-pen, Burgstaller 78)
* Mainz 3 (Maxim 2, Bell 52, Latza 58) Hamburg 2 (Walace 9, Salihovic 90+2-pen)
* Hanover 1 (Sane 36) Frankfurt 2 (Haller 10, Rebic 89)
* Borussia Dortmund 2 (Aubameyang 4, 64-pen) RB Leipzig 3 (Sabitzer 10, Poulsen 25, Augustin 49-pen)
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