Down 21-13 late in the fourth quarter, Davidson (0-4) was threatening on a drive starting from its own 1. Sparked by a 29-yard rush by Spencer Perry and a 47-yard pass from Jonathan Carkhuff to Tim Hines, the Wildcats got to the Blue Hose 14.
Carkhuff was sacked, then picked off by Williams, who ran 76 yards to the 6. Rouse scored one play later with 2:53 remaining.
Carkuff, who threw for two touchdowns, was intercepted earlier by LJ Perry, who ran 66 yards for a 7-0 score.
Rouse started the run of 21 unanswered points for Presbyterian (2-3), capping an 85-yard drive with a 3-yard TD late in the third.
Cedric Byrd's 44-yard punt return to the Davidson 19 set up the Blue Hose's next touchdown.
Michigan coach Jim Harbaugh says young players at his camps this summer have him convinced that football has a bright future.
GameDay 100: During the Chick-fil-A Bowl in 2013, Texas A&M quarterback Johnny Manziel manages to stay on his feet, scrambling to buy time to complete the touchdown against Duke.
In the dog days of summer, some of the world's most popular sports figures take a crack at sports other than their own.
Kansas State will add experienced safety Dante Barnett to what it appears to be a very solid returning core in the secondary.
On a defense in desperate need of new playmakers, Mondeaux is one of the Ducks' and new DC Brady Hoke's best bets.
Former NFL executive and player Merton Hanks has been named senior associate commissioner of Conference USA. He will be responsible for managing the league's operations for football and baseball.