The Avila defense caused 16 Baker turnovers and held the Wildcats to just 23.5-percent from beyond the arc, 4-of-17.
With the loss, Baker falls to 9-17 overall and 3-12 in the HAAC, while Avila improves to 6-18 and 4-11 in the conference.
The Wildcats posted three double-digit scorers with EJ Carter and Tyrome Parker scoring 11 points and Eric Watson added 10.
Avila shot 45.5-percent from the field and was solid from the free-throw line shooting 75.9-percent with Johnson knocking down some big ones down the stretch. He finished the night shooting 10-of-17 from the field and 8-of-10 from the free-throw line.
Carter led Baker with six rebounds and Javeion Gray had nine points with two three-point field goals.
The Wildcats will hit the road next time out, as they face Evangel on Saturday, Feb. 22 in Springfield, Mo.