The Wildcats came within 58 seconds of notching their first shutout of the season, but Daniel Parr connected with Kareem Coles Jr. for a 12-yard TD to provide the final margin of victory.
Hughes started the scoring for the Wildcats (2-2) when he capped an eight-play, 42-yard drive with a 45-yard field goal at the 11:16 mark of the first quarter. Dylan Laube's 6-yard TD run with 15 seconds left in the quarter put New Hampshire up 10-0.
Hughes added a 39-yard field goal in the second quarter and a 38-yarder in the third to put the Wildcats up 16-0.
New Hampshire put the game out of reach when Pop Lacey picked off a Parr pass at the Wildcats' 43-yard line. An unsportsmanlike conduct penalty on Lacey pushed the ball back 15 yards, but Gray broke loose for a TD on the next play.
Brosmer completed 17 of 31 passes for 202 yards, while Gray finished with 99 yards on 10 carries.
Parr was 14-of-32 passing for 183 yards and two interceptions.
New Hampshire had 433 yards of offense and held the Dukes (2-2) to 233, including just 50 yards on 23 carries on the ground.
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