Drake (5-3, 4-1 Pioneer Football League) won its 19th straight league home game.
Butler (3-5, 1-4) took a 17-14 lead late in the third quarter on Sam Schrader's 9-yard touchdown run. They recovered an on-sides kick, but Jon Treloar missed a 47-yard field goal.
Drake then marched down the field, going 70 yards in 12 plays, culminating with Wilkins' 2-yard score.
Andy Rice's 22-yard first quarter touchdown pass to Lee Snell gave Drake a 7-0 lead. Butler responded with Malcolm Weaver's 4-yard scoring toss to Brando Collins in the second. Treloar hit a 22-yard field goal and Butler led 10-7 at intermission.
Butler was driving midway through the third, but Drew Ormseth picked off Weaver and went 30 yards for the score as Drake went up 14-10.