Cuthbertson made all four of his field goal attempts, including 3 of 3 from 3-point range.
The Spartans opened the second half on a 7-0 run and led 35-26 with 16:35 left. A Cuthbertson 3 pushed the lead past double figures and a second Cuthbertson triple extended it to a game-high 18 points (55-37) with 6:54 remaining.
Navy (8-4) tried to battle back late, cutting the lead to 62-54 after two Jace Hogan free throws with 1:26 to go, but closest the Midshipmen got was seven.
Hogan had 14 points and 12 boards to lead Navy.