Bayern have now gone 37 league matches since their last defeat, at Bayer Leverkusen in October 2012, breaking Hamburg's previous record of 36 from January, 1983.
"The record is unbelievable, it's not easy to go 37 games without defeat. Congratulations to the club," said Bayern coach Pep Guardiola, who took charge in June.
"I have noticed that every game is a lesson for me in understanding my team." Guardiola's Bayern face their biggest test in a fortnight when they travel to second-placed Borussia Dortmund in a repeat of last season's Champions League final.
"Dortmund will be a good, good test for us and our level," added Guardiola. Guardiola also set a personal record as he celebrated his 12th league match without defeat -- the best start by a new Bundesliga coach in the league's history with 32 points.
The Champions League holders opened the scoring at Munich's Allianz Arena when Germany centre-back Jerome Boateng headed home from a corner after just five minutes.
France winger Franck Ribery then smashed home a direct free-kick on 42 minutes before Germany's Thomas Mueller netted a penalty in the fifth minute of injury time.
Bayern, who have won 31 of their last 37 Bundesliga matches, were without Germany's Bastian Schweinsteiger, who will miss the forthcoming internationals against Italy and England with an ankle injury.
It was Bayern's second milestone of the week after they equalled Barcelona's record from the 2002/03 season of nine consecutive Champions League wins with a 1-0 at Viktoria Pilsen.
Breaking records is nothing remarkable for Bayern these days having set or equalled 25 league records under Guardiola's predecessor Jupp Heynckes last season.
Heynckes stood down in May, with his side unbeaten in their previous 25 league games, after Bayern won the treble of European, cup and Bundesliga titles last season.
Bayern also extended their lead at the top of the table to four points as second-placed Borussia Dortmund went down 2-1 at VfL Wolfsburg.
It was Dortmund's second defeat of the week after losing to 1-0 at home to Arsenal in the Champions League.
After Germany winger Marco Reus put Dortmund ahead with a thunderbolt of a free kick on the stroke of half-time, Wolves hit back to pick up their fourth straight victory to leave them fifth.
Swiss defender Ricardo Rodriguez smashed home a free kick before Croatia striker Ivica Olic hit a great goal in off the far post with 20 minutes left.
"We gave away too many free-kicks, which allowed the opposition some practive in taking them," lamented Dortmund coach Jurgen Klopp, adding centre-back Neven Subotic has a suspected cruciate knee injury.
"Olic's goal was a dream. It should have been blocked, but that didn't happen. Neven Subotic's injury is terrible news."
Third-placed Bayer Leverkusen are level with Dortmund on 28 points after beating Hamburg 5-3 with South Korea's star striker Son Heung-Min scoring a hat-trick.
Son scored after nine and 16 minutes before hitting his third on 55 minutes, before setting up Stefan Kiessling for Leverkusen's fourth.
Borussia Moenchengladbach scored three goals in the last 18 minutes to come from behind and seal a 3-1 win at home to Nuremberg to stay fourth in the table.
Schalke bounced back from their Champions League defeat at Chelsea as they came from behind to beat Werder Bremen 3-1 with Ghana midfielder Kevin-Prince Boateng netting two headers.
Hertha Berlin stayed seventh after their 3-2 win at Hoffenheim with Colombia's Adrian Ramos scoring two goals, including the winning goal when he headed the winner six minutes from time.