Robert Lewandowski's brilliant goal - his 10th in the league this season - helped Bayern Munich comfortably overcome Hoffenheim and consolidate their place at the top of Bundesliga in front of a filled to capacity Allianz Arena.
Bayern boss Julian Nagelsmann was absent from the touchline against his former club after testing positive for Covid-19, with assistant coach Dino Toppmoller standing in.
Lewandowski somehow failed to score from six yards out as Bayern came flying out of the traps, but Serge Gnabry finally gave the hosts lift-off in the 16th-minute when he finished a fine team move, moments after he had a goal disallowed by VAR.
Lewandowski brace helps Bayern pull clear of Dortmund at top of table
The Poland international would make amends when he doubled their advantage with a special strike from 25 yards in the 30th-minute.
Hoffenheim goalkeeper Baumann kept his side in the game when he repelled Lewandowski at point-blank range just before half-time.
After Bayern put five past Leverkusen last weekend, the signs looked ominous for Hoffenheim. However, the hosts took their foot off the gas and were almost punished when Sebastian Rudy inexplicably missed the target against his former club.
Bayern came to life again in the last 10 minutes as substitutes Eric Maxim Choupo-Moting and Kingsley Coman marked their cameos with late goals to seal a slightly flattering victory.
However, there was still time for Lewandowski to make it a hat-trick of missed gilt-edged opportunities as he blazed over the bar after rounding the Hoffenheim goalkeeper.
The Bavarians remain top of the Bundesliga table after nine games with 22 points from a possible 27, one point ahead of second-placed Dortmund, who won 3-1 at Arminia Bielefeld.
TALKING POINT - Bayern once again demonstrate scary strength in depth
Today was another reminder of Bayern's scary strength in depth. His wonder strike aside, Lewandowski didn't have the best of days in front of goal, but Nagelsmann - who was sending instructions to his coaches from his kitchen - would have nothing to fear as his supporting cast stepped up, allowing the Bundesliga champions to chalk up an emphatic win that slightly flattered their performance.
Gnabry continued his rich vein of goalscoring form with his sixth league strike of the season. Having been afforded to rest some key players ahead of a packed schedule, Choupo-Moting and Coman came off the bench to kill off Hoffenheim's hopes after the visitors had provided a considerable threat after the restart.
Ultimately, it was another productive day for the Bavarians, who have now won three successive league games as they continue to lead the way in the early Bundesliga table.
MAN OF THE MATCH - Serge Gnabry (Bayern Munich)
The 26-year-old is in great form and he was Bayern's standout player, full of endeavour. Looked like creating something magical every time he received the ball.
Bayern Munich: Neuer 6, Pavard 6, Upamecano 8, Hernandez 6, Richards 6, Sabitzer 6, Kimmich 7, Gnabry 8*, Muller 8, Musiala 7, Lewandowski 7.. subs: Sule 6, Sane 5, Coman 7, Choupo-Moting 7, Tolisso 5.
Hoffenheim: Baumann 7, Posch 6, Grillitsch 5, Richards 5, Akpoguma N/A, Samassekou 5, Geiger 5, Raum 6, Bruun Larsen 5, Bebou 5, Kramaric 5.. subs: Stiller N/A, Rudy 5, Adamyan N/A, Skov 5.
16' - GOAL! Bayern Munich 1-0 Hoffenheim (Serge Gnabry): That felt inevitable! And this time it will count! After a period of short, one-touch passing, Musaiala switches it to Gnabry, and from a tight angle he squeezes his shot through the legs of Baumann! It's his sixth goal of the season!
30' - GOAL! Bayern Munich 2-0 Hoffenheim (Robert Lewandowski): That is majestic from Lewandowski! The Bavarians hit the hosts with a swift counter-attack! Muller outmuscles Richards, he tees up Lewandowski and he arrows an unstoppable shot into the corner from 25 yards! No goalkeeper in world football is saving that!
82; - GOAL! Bayern Munich 3-0 Hoffenheim (Eric Maxim Choupo-Moting): The visitors make a mess of attempting to clear their lines from the resulting corner, as Kramatic hits his clearance straight at Upamecano, and Choupo-Moting is on hand to slot home to mark his cameo with a goal! That seals it!
87' - GOAL! Bayern Munich 4-0 Hoffenheim (Kingsley Coman): A simple ball over the top from Upamecano unlocks Hoffenheim's defence and Coman has time to pick his spot, comfortably beating Baumann with a composed finish.
Manuel Neuer won his 300th Bundesliga game (in his 447th game). Only Oliver Kahn has more wins in Bundesliga history (310).
Sane stunner breaks Arminia resistance and sets new record for Bayern
Lewandowski and Coman on target as Bayern beat Dynamo Kyiv
FC Bayern Munich
TSG 1899 Hoffenheim