Wilkins had 88 yards rushing and Rice added 151 through the air with a touchdown to lead Drake (1-1) offensively.
Benjamin Tesson missed a 37-yard field goal as time expired that would have given Drake the victory in regulation.
An 11-yard touchdown catch by Saubert gave Drake a 7-0 lead in the first. Quarterback Devonte Black answered later in the quarter with 1-yard TD run for Truman State, who were playing their first game of the season.
Black also threw for 148 yards on 17 of 31 passing.