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.