The champions, looking for a record fourth straight Bundesliga title, are on 40 points and, with three games left, will go into next month's winter break in top spot if second-placed Borussia Dortmund, on 29, fail to beat VfB Stuttgart on Sunday.
A day after reporting record profits, Bayern were equally sparkling on the pitch, looking fresh after their midweek 4-0 mauling of Olympiakos in the Champions League and despite key injury absences including Arjen Robben, Douglas Costa, David Alaba, Mario Goetze and Thiago Alcantara.
Coach Pep Guardiola fielded his 14th different starting eleven in 14 league games this season but they were dominant from the start, striking twice late in the first half with Mueller nodding in from a Medhi Benatia header in the 34th minute to take his league goal tally to 13 in 14 matches.
Frenchman Coman added another four minutes before halftime and Poland striker Robert Lewandowski, who hit the woodwork in the first half, had a golden chance in the 53rd, having been left unmarked in front of goal but was betrayed by his poor first touch.
Bayern's domination can be gauged by the fact they enjoyed more than 70 percent possession and had 24 shots on goal to Hertha's four.
"The team deserves a big compliment because we had a lot of injured players," Guardiola said.
"We only allowed them one chance in the entire game. We did it really well in the first half. I know how difficult it is to be ready every three days."
U.S. international Fabian Johnson scored twice, including a superb 87th minute equaliser after a fine run to rescue a 3-3 draw for Borussia Moenchengladbach against Hoffenheim and maintain coach Andre Schubert's unbeaten run after nine games. Gladbach are fourth on 23, one point behind VfL Wolfsburg, who take on Augsburg on Sunday.
Hamburg SV won 3-1 at Werder Bremen in their northern derby to climb up to sixth on 21.
The visitors were two up midway through the first half before Werder's Anthony Ujah pulled a goal back after the break and Nicolai Mueller sealed Hamburg's victory in the 68th minute.
Struggling Hanover 96 crushed promoted Ingolstadt 4-0, firing in three goals in the opening 24 minutes for their first win in three league games while Eintracht Frankfurt had striker Alexander Meier sent off in a 2-1 defeat by Mainz 05.
(Reporting by Karolos Grohmann, editing by Ian Chadband)
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