Blake Simmons added 13 points for Evansville (12-18, 5-12 Missouri Valley Conference) and Egidiju Mockevicius was held scoreless, but grabbed 10 rebounds. Balentine made four 3-pointers as Evansville hit 6 of 12 from deep.
Evansville ended a three-game losing streak and pulled itself out of the conference cellar.
Ten players scored for Drake (14-15, 5-12) but none were in double-figures. Daddy Ugbede had seven, on 3-of-8 shooting, and Jordan Daniels made two of Drake's four 3-pointers, in a combined 16 attempts.
The Bulldogs made just 6 of 20 second-half baskets and were limited to 18 points after the break.
Evansville held the Bulldogs without a basket for nearly 11 minutes, spanning both halves, and led by double-digits for the final 10 minutes.