A shocking own goal from Dortmund goalkeeper Gregor Kobel, as well as two trademark poacher's finishes from Thomas Mueller had Bayern 3-0 up by the 25th minute.
Kingsley Coman added a fourth shortly after half-time to send Bayern two points clear of the visitors despite two late consolation goals.
Dortmund came into the match in the unfamiliar position of first place, one point ahead of Bayern, who fired coach Julian Nagelsmann in favour of Tuchel last week.
Tuchel, who won a German Cup title during a two-year stint in charge of Dortmund, only had one training session with Bayern but it was Kobel who gifted them a flying start in the 13th minute.
The 'keeper, who returned after a five-week injury layoff, charged out of his box to try and clear Dayot Upamecano's long pass, but could only make the faintest of contacts with the ball before watching helplessly as it rolled into the net.
Mueller scored from a corner just five minutes later and pounced when Kobel spilled Leroy Sane's shot five minutes after that.
Unlike earlier in the season when Dortmund came from 2-0 down to draw 2-2 at home with Bayern, there would be no miracle comeback this time around, with Coman sliding the ball under Kobel early in the second half.
Emre Can converted a consolation penalty after Serge Gnabry fouled Jude Bellingham in the box, while Dutch forward Donyell Malen added a second for Dortmund in the last minute of normal time.