After trailing 21-7 before halftime, Lafayette (1-3) outscored Wagner (0-3) 28-3 the rest of the way.
Reed completed 23 of 34 passes for 308 yards - the first 300-yard game for a Leopards quarterback since 2013. Freshman Joey Chenoweth caught nine passes for a career-best 109 yards with a score.
Wagner's Alex Thomson, who'd put up 142 yards and two touchdowns by halftime, was harried in the second half. He finished 15 of 23 for 219 yards, two touchdowns, two interceptions, and was sacked once.
After Wagner regained the lead, 24-21, on a field goal, the Leopards launched a nine-play drive, capped by a Reed two-yard toss to Mark Mrazek for the go-ahead TD. Reed ran 10 yards untouched on a bootleg for the final score.
AP college football website: http://collegefootball.ap.org