The Stags shot 55.9 percent from the field, hit 12 3-pointers, and finished with 19 total assists as a team.
After Connor Boehm hit a jumper to give Dartmouth (4-8) a 59-58 lead with 11:48 left in the game, Fairfield went on 17-6 run over the ensuing five minutes to grab a 75-65 lead. Seven of the 16 points came from Johnson Jr.
Dartmouth never seriously threatened the rest of the night.
Gilbert added a 3-point play to extend the Fairfield lead to a game-high 14 (97-83) with 35 seconds left.
Boehm finished with 24 points for the Big Green.