VMI (3-5) led by as many as six points in the second half, and held a 63-59 lead with about nine minutes left.
Army (5-2) responded with an 8-0 run to turn a four-point deficit into a four-point advantage to take the lead for good.
Army was 8 of 8 at the free throw line in the final two minutes.
The teams traded the lead back and forth in the first half, heading to the break tied 37-all.
Brown shot 8 of 17 from the floor. Walker converted 8 of 11 field goals and 7 of 10 free throws.
Army outrebounded VMI 45-31.