Trailing 21-7 at halftime, Wagner (1-3) made it a four-point game after scoring on a 39-yard field goal by Bryan Maley and an 18-yard pass from Brian Gehring to Ryan Owens.
Scheuerman put Lafayette (2-2) ahead 28-17 with a 27-yard TD run in the fourth quarter, but Gehring replied with a 25-yard TD pass to Bryant Watts to pull within five.
Scheuerman broke away on a 55-yard TD run to put the game out of reach. He had 128 yards on 29 carries.
Searfoss was 14 of 23 for 173 yards passing, with scoring passes of 9 yards to Matt Mrazek and 24 yards to Justin Adams.
Gehring was 11 of 31 for 179 yards and three TDs, including a 46-yard TD pass to Brandon Peoples.