But the Cardinals' Anthony Mullins ran the ensuing kickoff 97 yards for a touchdown making it 26-16.
Josh Lee hit a 24-yard field goal making it 29-16 to end the quarter.
Nick West then led the Cardinals 69 yards in eight plays, capped by a 21-yard touchdown pass to Cody Edwards cutting the lead to 29-23.
Drake countered with its own eight-play drive, which ended with a 22-yard touchdown toss from Rice to Eric Staubert with 9:08 left. The two-point conversion extended the lead to 37-23.
Wilkins, who had 110 yards rushing, concluded the Bulldogs' scoring with a 4-yard run.
William Jewell's Trejuan Mask had 114 yards rushing and 50 more receiving.