MTSU (4-3) sprinted out to a 6-1 lead before MSU responded, taking its only lead of the game 11-10 on a basket by Ketara Chapel.
The Blue Raiders answered with the game's next seven points and did not trail the rest of the way.
MSU was playing without the services of backup point guard Jerica James. James injured her shoulder in Saturday's semifinal round win over James Madison.
MSU converted 5 of 28 shots from the field in the opening half and trailed 30-15 at the intermission.
"I am proud of my kids. We have played very good teams and we have played hard against them. We have been tested three straight days," Schaefer said. "We are fortunate. We came here and won two games. You come here so you can learn about your team and address things before conference play begins."
The Blue Raiders ran the lead to 22 less three minutes into second half. An offensively flurry tightened the contest but the Bulldogs could not get over the hump.
"We are still learning," Schaefer said. "We are learning how to play and how to compete. I thought Katia May and Savannah Carter played their guts out tonight. (Winning two games here) shows growth in our program. To come here and compete and win two games against quality opponents is nothing but a positive.
"I am excited about this team. We have a chance to be quite a bit better. We need to get to the practice floor now and get better."
For the contest, the Bulldogs hit 16 of 55 shots from the field (29.1 percent), 2 of 7 shots from 3-point range (28.6 percent) and 14 of 23 shots from the foul line (60.9 percent). The Blue Raiders hit 22 of 49 shots from the field (44.9 percent), 2 of 11 shots from 3-point range (18.2 percent) and 16 of 25 shots from the foul line (64.0 percent).
MTSU held a 43-34 rebounding advantage. The Bulldogs had seven assists and 13 turnovers, while the Blue Raiders had 14 assists and 16 turnovers.
Carter led MSU with 14 points. Martha Alwal had six points, eight rebounds and three blocked shots. The blocked shots allowed Alwal set a new career MSU blocks record with 183. Alwal was also named to the all-tournament team.
MTSU received 25 points and 13 rebounds from Ebony Rowe and 14 points from Shanice Cason.
MSU hosts Louisiana-Lafayette at 7 p.m. Wednesday in the Humphrey Coliseum.