The Yellowjackets improved to 10-2 overall and a perfect 3-0 in the conference with the victory.
Despite a big eight-point lead at halftime, 40-32, the Wildcats couldn't hang on and were outscored 46-32 in the second half.
Tyrome Parker had a team high 20 points off the bench and EJ Carter and Todd Johnston each scored in double figures as well, with 11 and 10 respectively.
What helped the Yellowjackets pull through was there nearly perfect free-throw shooting, as they shot 88.2-percent, 30-of-34, and Baker went to the line just 18 times, going 11-of-18, for 61.1-percent.
Parker had three three-point field goals for Baker and Johnston had the other two, as BU went 5-of-14 from behind the arc.
The Yellowjackets had three players score in double figures and they shot just 40-percent from the floor, 22-of-55.
Baker will next take on Central Methodist on Monday, Dec. 16 at 7:30 p.m. in Fayette, Mo.