Army (7-6) shot 50 percent from the floor, finishing 24-for-48, and was 42.9 percent on 3-pointers.
Portland shot 42.3 percent, finishing 22-of-52 from the floor, and was 38.9 percent from beyond the arc.
Brown, who came in averaging 20.7 points, had just five at the half before erupting for 18 second-half points.
Trailing by five at the half, Portland took control early in the second half and had a 36-33 lead with 13:24 remaining.
Army regained the lead minutes later, but Watson then drilled a jumper to give the lead back to Portland at 40-39 with 10 minutes left.
The Black Knights then embarked on 21-10 run to gain control of the game.