With the win Baker moved to 6-5 on the year and dropped CMU to 7-7 and 0-3 in the HAAC.
EJ Carter again helped carry the 'Cats with his team high 14 points and was a perfect, 10-of-10 from the free-throw line. He also had seven rebounds.
Connor McDaniel was solid for Baker with his 12 points and four rebounds and Jared Fulks also scored in double figures with 11.
Baker was 23-of-28 from the free-throw line and held the Eagles to just 40-percent from the field and caused 17 turnovers.
Melvin Tillman was the only Eagle to score in double figures with his 25 points on 8-of-21 shooting.
The contest was close throughout, as Baker owned just a one-point lead at the break, 27-26, and outscored CMU, 37-34 in the second half.
Baker's bench outscored CMU's, 29-19, and Baker put up 28 points in the paint, while the Eagles scored 22 in the paint.
BU will hit the road again in its next game, as they take on Haskell on New Years Eve, Dec. 31 at 2 p.m.