Greene hit eight consecutive field goals in the second half and finished 12 of 18 from the floor, five of eight from behind the arc and seven of seven from the charity stripe. He tied Brian Hodges for the fourth-most points in a game for a Retriever, as Greene's former teammate had 36 at Morgan State on Nov. 27, 2006.
UMBC senior forward Darryl Proctor (District Heights, Md.) added 23 points and posted 10 rebounds to record his eighth double-double of the season.
New Hampshire was led by guard Alvin Abreu, who led four Wildcats in double figures with 20 points.
But UNH fought back, using a barrage of threes to climb within a single point on two occasions. Wildcat forward Radar Ongeutou's putback with 1:40 remaining cut the deficit to 77-76, but Greene hit two free throws 20 seconds later and UNH would misfire on a pair of three-point attempts down the stretch. UMBC wing Matt Spadafora (Richboro, Pa.) sealed the win with a pair of free throws with 14 seconds remaining.