Reed was 14 of 26 for 149 yards for the Leopards (1-1). Ross Scheuerman ran for 173 yards on 22 carries.
Jared Roberts began the scoring for Lafayette with a 38-yard interception return midway through the first quarter. Reed took it in from 5 yards for another TD and Lafayette's defense forced a safety to extend the Leopards' first quarter lead to 16-0.
Mark Dodd picked off another Luke Brumbaugh pass early in the second quarter for another Lafayette score. Adin Greenfield put the final points on the board with a 17-yard touchdown run early in the fourth.
Hunter Khaleghi's 25-yard field goal was the only score for Robert Morris.
The Colonials (0-3) were held to 102 total yards. Brumbaugh was 11 of 23 for 60 yards and three interceptions.