The Bulldogs (4-2) took control early with a 30-15 lead at the 5:56 mark. However, the Black Knights (3-3) allowed only two more points, an Alex Francis dunk with 1:47 left, to make it 32-22 at the half.
Ella Ellis hit a 3-pointer to open the second half, but that was as close as Army -- which had won the previous five games in the series -- would get.
Bryant, fresh off beating Boston College 56-54 for its biggest win in program history, also posted its first win in eight tries against a Patriot League opponent.
Alex Francis added 17 points and Joe O'Shea 12 for the Bulldogs.
Ellis scored 16 to lead Army, which was coming off an 86-83 overtime loss to Yale.
Mississippi State freshman guard Malik Newman will withdraw from the NBA draft, but sources told ESPN he might explore other opportunities besides returning to Mississippi State.
Seton Hall sophomore Isaiah Whitehead will stay in the NBA draft and not return for his junior season.
Washington State's trio of Josh Hawkinson, Conor Clifford and Ike Iroegbu have withdrawn from the NBA draft and will play their senior season with the Cougars.