With the win, Baker improves to 7-3 overall and 1-0 in the HAAC and has won three straight, while Avila falls to 1-6 and 0-1 in conference play.
The Eagles came into 2012-13 ranked No. 20 in the NAIA Coaches' Top 25 Poll but have struggled to pick up more than one victory this season.
Baker traded baskets with Avila early on and managed just a 10-9 lead with 11:47 to go in the first half, when Kyrstie Ehm nailed a three-point basket.
But after that point, the Wildcats went on a 10-2 run and extended its lead to 20-11 with 8:22 left in the half.
Avila rallied late with buckets from Jessica Smith and Cassie Bruner and entered the half down just four, 36-32.
The Eagles eventually tied things up at 39-39 with a three-point shot by Michaela Brinkley, but the Wildcats started to pour it on after that point with an 8-0 run to go up, 47-39 and Baker never game up the lead again.
BriAnna Garza went off for 23 points, four assists and nailed three baskets from behind the arc and teammates Rece Huddlin and Alisha Fanshier each scored in double figures with 15 and 13 respectively.
Huddlin had a double-double with her 15 points and 10 rebounds and Wildcats were nearly perfect from the free-throw line shooting 85.7-percent from the line at 12-of-14.
Baker will next take on Missouri Valley this Saturday, Dec. 1 at 2 p.m. at the Collins Center for its next HAAC contest.