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 league matches.
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 season's tally to nine. Bayern completed the rout in stoppage-time when Joshua Kimmich scored on the break.
DORTMUND LOSS
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.
The Gabon international put the hosts ahead after four minutes but Leipzig, playing without leading striker Timo Werner, struck three times before the dismissal of Stefan Ilsanker.
His departure levelled the playing field after Dortmund's Sokratis Papastathopoulos was sent off two minutes after the restart.
Aubameyang pulled one back through a penalty in the 64th for his 10th goal of the season but it was not enough to avoid defeat.
"It was a gripping game but not a great one and certainly not good football," Dortmund coach Peter Bosz said. "We played a very bad first half."
Hoffenheim dropped to fourth after twice leading against Augsburg but conceding a last-gasp goal to earn a 2-2 draw that left them on 15 points. Leipzig are third on 16.
(Reporting by Karolos Grohmann,; Editing by Clare Fallon and Ed Osmond)
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