Jackson had 25 points with six 3-pointers for Rice (11-18, 8-9 Conference USA) while Gearhart was 5 of 6 from downtown and finished with 23 points.
Rice used an 11-point run early, including a pair of Seth Gearhart 3-pointers, to open an 18-9 lead. UTSA tied it at 25, but the Owls scored the next six points and led 46-35 at the break.
UTSA battled back and made it a one-point game on Jeromie Hill's 3-pointer with 4:03 left. Keon Lewis' 3 made it 75-74 with four seconds to go, but he fouled Gearhart on the inbounds play and Gearhart made 1 of 2 at the line for a two-point lead.
UTSA (13-15, 7-10) was led by Lewis' 22 points and Hill ended with 20.