It was Muller's 428th league appearance for the club, one more than his namesake, the great Gerd Muller, and the most for any outfield player at the club.
Only goalkeepers Oliver Kahn (429) and Sepp Maier (473) have played more Bundesliga games for Bayern.
Muller capitalised on a botched backpass from Bochum defender Saidy Janko to break the deadlock of Saturday's match in the 41st minute with his fourth league goal of the season. He now has 141 altogether.
Bayern substitute Kingsley Coman finished some fine combination play in the 64th and Serge Gnabry made it 3-0 with a penalty in the 73rd after he was fouled by the luckless Janko.
It kept Bayern one point clear of Union Berlin, who came from behind to beat Leipzig 2-1 away in the late game.
Bayern next visit Paris Saint-Germain in the Champions League. Bayern coach Julian Nagelsmann was evidently thinking of Tuesday's game when he took Muller off at halftime and also gave some time off to Joao Cancelo, Jamal Musiala, Eric Maxim Choupo-Moting and Leroy Sane.
Nagelsmann said he took Muller off as a precaution because of a calf problem and he thinks the veteran will be fit for Paris.
Union ended Leipzig's 18-game unbeaten run across all competitions with their win.
Leipzig hadn't lost at home in the Bundesliga since their previous 2-1 loss on Union's visit last season.
The visiting fans stayed silent for the first 15 minutes in protest against Leipzig, who are disliked by rivals as they're seen as a marketing tool for Red Bull since their formation by the energy drinks manufacturer in 2009.
Benjamin Henrichs let fly to put Leipzig ahead in the 24th, but the visitors improved in the second half and Janik Haberer equalised with a perfectly struck volley from the edge of the penalty area in the 61st.
Leipzig defender Mohamed Simakan then conceded a penalty for attacking the ball with his arm. Robin Knoche scored what proved to be the winner from the spot in the 72nd.
Borussia Dortmund coach Edin Terzic's changes again paid off in a 2-0 win at Werder Bremen that stretched the team's winning run to six games across all competitions this year.
"We've always said, there are players who start for us, players who finish games for us, and players who decide games for us," Terzic said of substitute Jamie Bynoe-Gittens, who broke the deadlock in the 67th.
"It's the 10th time in the Bundesliga that a player has scored for us from the bench. We also had it in the Champions League and cup."
The visitors were held at bay until Terzic brought Bynoe-Gittens on for Gio Reyna. The English teenager scored a minute later, firing inside the top corner to beat Pavlenka.
Julian Brandt sealed the win with a brilliant finish in the 85th after good work from Raphael Guerreiro to set him up.
Pellegrino Matarazzo's debut as Hoffenheim coach ended with a 3-1 defeat at home to Bayer Leverkusen.
Stuttgart defender Dan-Axel Zagadou conceded two penalties and Vincenzo Grifo scored both goals in Freiburg's 2-1 victory, while Lee Jae-sung scored twice to help Mainz defeat Augsburg 3-1.
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