Sherman hit 7 for 10 from the field, including the go-ahead bucket midway through the second half. Hill shot 6 of 9 with two 3-pointers and hauled in 12 rebounds. They got help from Ryan Bowie's 16 points and Keon Lewis' 10 as UTSA (10-9, 4-4 Conference USA) shot 50 percent from the floor on 44 attempts.
Trailing by seven at the break, UTSA opened the second half with a 15-3 run that included eight straight points from Sherman to take a 46-41 lead with 14:15 left. Sherman gave the Roadrunners the lead for good 53-52 with a dunk five minutes later and they pulled away down the stretch.
Perrin Buford and Darnell Harris led Middle Tennessee (12-9, 5-3) with 15 points apiece.