Conley Wilkins rushed for a career-high 152 yards on 13 carries and had a 100-yard kickoff return after Stetson's field goal to give the Bulldogs (2-2) a 17-3 lead at the half.
Thibault completed 16 of 33 passes but was picked off by Eric Martin of the Hatters (1-2) three times in the first half.
Thibault connected with Lee Snell for an 11-yard touchdown in the second quarter, Zach Zlabish for 12 yards in the third and A.J. Spitz for 55 yards in the fourth. Andrew Clifford threw a 7-yard touchdown to Connor Ostrander to close the scoring.
Stetson finished with 178 yards passing but with Drake getting seven sacks, the Hatters finished with zero rushing yards.
AP College Football website: www.collegefootball.ap.org