Shai Werts rushed 31 times for 124 yards and threw for 93 yards for Georgia Southern (0-2). Wesley Fields had 15 carries for 52 yards.
Trevor Knight completed 13-of-22 passes for 129 yards and ran for 55 for UNH (2-0), and Neil O'Connor caught 11 passes for 118 yards.
Miscues hurt the Eagles on two promising drives in the first half. GS went right down the field on its first possession of the game, but an errant pitch by Werts found the turf and was recovered by New Hampshire's Brian Carter at the Wildcat 30-yard line.
The Eagles drove down to the UNH 22-yard line midway through the second quarter but were backed up by the officials for an illegal chop block. GS had to settle for a 43-yard field goal try by Tyler Bass, which sailed wide right. Georgia Southern had four drives of 10-plays or more and held an 11-minute advantage in time of possession in the contest.
New Hampshire scored on its first two possessions of the game. Gray picked up a first down on 3rd-and-6 from the GS 17-yard line with a 7-yard run, and Knight hit O'Connor on a pop pass for a 10-yard touchdown on the following play. Knight then threw to Justin Malone-Woods on the swinging gate play for the two-point conversion and an 8-0 lead.
Gray made it 15-0 with a 2-yard run on the Wildcats' next offensive series. A 27-yard pass from Knight to O'Connor on the first play of the drive helped set up the score. UNH tacked on another touchdown with 3:48 left in the half when Knight and O'Connor hooked up for an 18-yard touchdown. Gray keyed that touchdown drive with a 47-yard scamper, and the Wildcats owned a 22-0 edge at halftime.
Late in the third quarter, Georgia Southern drove down to the UNH 19-yard line before moving backwards due to some nice plays by the Wildcat defense. Bass got the Eagles on the scoreboard with a 43-yard field goal, the first of his career.
Trailing 22-5, Werts broke off a 42-yard run to set up a 5-yard touchdown run by L.A. Ramsby with 6:18 to play. New Hampshire converted two first downs on their ensuing drive and ate up 4:01 of clock to put the game away.
Georgia Southern outgained New Hampshire 326-274, including 192-72 in the second half.