The visitors found themselves down to 10 men just 11 minutes into the game when Sven Kums hauled Robert Lewandowski down by his shirt in the box.
Kums was shown a red card for the challenge, which also gifted Bayern a penalty, and Lewandowski stepped up and calmly slotted into the bottom left-hand corner of the Anderlecht goal.
Both sides enjoyed a number of chances throughout the rest of the first half as Corentin Tolisso blasted over the bar in the 32nd minute, while Nicolae Stanciu fired wide of Bayern's post from inside the box.
The second half brought more concrete chances, however, as Stanciu rattled the post with his 49th-minute effort, while Lewandowski and Niklas Sule tested Matz Sels in the Anderlecht goal.
Bayern were able to find a second goal in the 65th minute, with Joshua Kimmich displaying great vision to find Thiago Alcantara, who duly buried the ball from close range into the back of the net.
With Anderlecht labouring to find a way back in the game, Carlo Ancelotti's charges added a well-deserved third late on, Kimmich collecting Jerome Boateng's through-ball and firing into an empty net.