Rice was 11 of 15 and 216 yards for the Bulldogs (3-3, 2-1 Pioneer). Wilkins ran for 110 yards on 13 carries.
Wilkins picked up two scores in the first half, one from 18 yards and the second from 4. Rice kept pace with a pair of touchdown passes - one to Matthew Denning and another to Keegan Gallery - and Benjamin Tesson kicked a 25-yard field goal to give the Bulldogs a 30-0 halftime lead.
Rice found Denning once again for a 27-yard TD early in the second quarter and the Bulldogs had a 37-0 advantage.
The Drake defense held Davidson to just 163 total yards offense.
John Cook finished with 87 yards passing, including a touchdown, for the Wildcats (1-6, 0-3).