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.