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.
Auburn senior receiver D'haquille Williams has been dismissed from the team.
Alabama coach Nick Saban took exception with the media's outlook on his team prior to Saturday's win at Georgia, lashing out at those who "buried" the Crimson Tide.
Despite a 1-4 start to the season and a 7-11 record since taking over at Texas, coach Charlie Strong has ongoing support from school officials and key boosters, according to several sources.
Questions are being raised about the transparency of the daily fantasy industry after a DraftKings employee won $350,000 in a weekend contest on FanDuel.
As much confidence as LSU coach Les Miles expresses in the abilities of his receivers, he has apparently decided to see if the threat of lost playing time sharpens their focus.
Michael Brewer, originally expected to miss eight to 10 weeks, broke his left collarbone in the Hokies' season-opening loss to No. 1 Ohio State.