Bayern, looking fresh after their midweek 4-0 mauling of Olympiakos in the Champions League to reach the knockout stage, struck twice late in the first half with Germany international 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 after Robert Lewandowski had hit the woodwork.

Gladbach are fourth on 23 points, one behind VfL Wolfsburg, who take on Augsburg on Sunday.

Hamburg SV won 3-1 at Werder Bremen in their northern derby. The visitors were two up midway through the first half with goals from Ivo Ilicevic and Michael Gregoritsch before Werder's Anthony Ujah pulled a goal back after the break and Nicolai Mueller sealed Hamburg's victory in the 68th minute.