The Wildcats (7-4) trailed Dartmouth (3-6) for the first several minutes of the game, but a 12-0 run sparked by Iba Camara changed that. Camara opened and closed the run with layups, and Leissner scored five points. Camara finished with nine points and 12 rebounds.
Joe Bramanti dished eight assists.
Cold stretches hampered the Big Green, who shot a season-low 28 percent (16-for-57). Leading scorers Connor Boehm scored four points - all on free throws - and freshman Evan Boudreaux was held to season lows of five points and four rebounds.
Guilien Smith led Dartmouth with 12 points.
New Hampshire outrebounded Dartmouth 47-31 - including 35 defensive boards - and notched 14 assists on 26 field goals while limiting Dartmouth to three assists, its fewest since 2009.