Broome finished on 10-of-11 shooting and had four rebounds and two steals. Evan Kelley was 6 of 10 from the floor and had 16 points for the Pioneers, who made 28 of 58 shots from the floor for 52.8 percent.
Phil Gaetano dished out seven assists for Sacred Heart (6-4).
Matt Miller hit a 3-pointer to give New Hampshire a 21-16 lead with 8:49 left in the first half. The Pioneers answered with a 19-4 run to take a 35-25 lead at the break.
In the second half, Tanner Leissner's jumper pulled New Hampshire within 46-43 with 12:48 remaining. A 14-2 run stretched the Pioneers' lead to 60-45 with 7:55 left.
Leissner and Daniel Dion scored 12 points apiece to lead New Hampshire (6-4).