The Wildcats turned the ball over 25 times and dropped its third straight contest, falling to 6-4 overall and 0-1 in the HAAC, while Avila improved to 4-3 and 1-0 in the HAAC.
Avila did a nice job hanging on to the ball, only turning it over 13 times and the Baker defense did a nice job throughout the night, holding the Eagles to poor shooting from the outside, holding Avila to just 7.1-percent from behind the arc, shooting 1-of-14.
The Eagles also shot just 36.4-percent from the field overall, 24-of-66, and 58.6-percent from the free-throw line, 17-of-29.
The Wildcats had three players score in double figures with Ben Steinlage leading the team with 12 and Julian Mills poured in 10 and Corey Anderson had 11.
With a run late in the first half and a bucket with five seconds to go until the break by Steinlage, Baker entered the half down just one, 31-30.
But out of the break, Avila went on a 10-0 run and led, 41-30, just 4:15 into the second half and never gave up the lead.
Baker did cut that lead to three points at 55-52, when Anderson nailed a three-pointer with 1:57 left in the game.
But, Avila nailed some key free throws down the stretch and took home the seven-point win.
Samer Jassar had a solid overall game with seven points, seven rebounds and a season high three blocks for Baker.
The Wildcats will next take the floor on Saturday, Dec. 1 at 4 p.m., as they return home to take on Missouri Valley at the Collins Center.