Cheek scored on a sneak on the first drive of the game. Jalen Greene capped the first-half scoring on a 7-yard power run with 31 seconds to go, giving Elon a 24-9 lead. Malcolm Summers had a 21-yard scoring run early in the second quarter.
Skyler Davis accounted for all of the fourth-quarter scoring on field goals of 18 and 30 yards for Elon.
Marcus Willoughby had three sacks for Elon (3-1, 1-0 Colonial Athletic Association), which held New Hampshire to 218 total yards.
Sean Coyne pulled UNH to 14-9 on a 25-yard run early in the second half, but the Wildcats' 2-point conversion attempt was no good.
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Georgia's Kirby Smart, LSU's Ed Orgeron and Coastal Carolina's Jamey Chadwell all shared their thoughts on the possibilities of an expanded College Football Playoff.
Ex-Colorado QB Sam Noyer heads to Oregon State for final season
Former Colorado quarterback Sam Noyer will use his final year of eligibility at Oregon State.
College Football Playoff expansion: 12-team historic simulations, storylines and more
Bill Connelly crunches the numbers using SP+ to figure out the most likely scenarios for how a 12-team playoff would have played out since 2014.
Latest on Bo Schembechler ignoring warnings of sexual misconduct from doctor
Michele Steele reports on claims that the late Bo Schembechler ignored warnings about former team doctor Robert Anderson's sexual assaults.
Herbstreit calls CFP expanding to 12 inevitable and for the best
Kirk Herbstreit joins SportsCenter to discuss the College Football Playoff possibly expanding to 12 teams.
Former Michigan football players say coach Bo Schembechler ignored warnings, son's complaint about doctor's abuse
Former Michigan football players Dan Kwiatkowski and Gilvanni Johnson, who have told investigators they were molested by former team doctor Robert Anderson, said head coach Bo Schembechler ignored their warnings at the time about abusive treatments.