Brett Roseboro added 13 points and seven rebounds, and Adrian Satchell and Chase Plummer scored 11 apiece to help UMBC (3-13, 1-2) snap an eight-game losing streak.
Ahead 33-29 at halftime, UMBC pushed the lead to 41-31 when Cook made a layup with 16:53 remaining.
New Hampshire (4-11, 0-3) cut the deficit to 50-44 at the 9:30 mark, but the Retrievers responded with a 12-4 run capped by Brian Neller’s jumper with 5:07 left to play.
UMBC maintained a double-digit lead the rest of the game.
The Retrievers shot 51.1 percent (24 for 47) while holding the Wildcats to 33.3 percent (21 for 63) shooting for the game.
Patrick Konan scored 19 points to lead the Wildcats, who have now lost six straight games.