Chasson Randle added 15 points for the Cardinal (5-3), who had lost three of their previous four games.
Prince Obasi recorded career highs with 18 points and eight rebounds for the Redhawks (2-2). Redshirt freshman Deshaun Sunderhaus had 12 points and a career-high 11 rebounds.
Brown was 6 of 9 from the field and also matched his career high with six rebounds.
Roscoe Allen hit a pair of free throws with 6:36 remaining to play to put Stanford ahead, 49-48.
Louis Green hit a jumper to bring Seattle even at 50, but the Cardinal went on a run and maintained the advantage.
The Redhawks led 36-29 just over two minutes into the second half.
Seattle led at halftime, 30-27.