Mayo scored 22 points and Knight provided 20, nine rebounds and eight assists as Milwaukee ended its lengthy skid.
John Henson had a double-double of 13 points and 13 rebounds.
Giannis Antetokounmpo helped out with 10 points and seven rebounds for the Bucks.
The Celtics were paced by Jared Sullinger with 21 points and 14 rebounds.
Notable deaths of 2014 [PHOTOS]
UPI Sports Results for September 19, 2014