Taking advantage of her own offensive rebounds, Brown scored 13 points in the second half as Arizona (5-0) took a 68-52 lead and ran a 12-2 stretch.
Santa Barbara (3-2) went on a 12-1 spurt behind a pair of buckets from Kayte Christensen, but a Julie Brase 3-pointer halted the Gauchos' momentum. Brase added two free throws to put Arizona ahead by 10 with 4:31 left.
Santa Barbara pulled to 80-76 with 1:17 remaining on a turnaround jumper from Christensen, but Reshea Bristol made two free throws and Brown broke free for an uncontested layup to seal the Arizona win.
Brown snagged seven rebounds. Brase added 14 points for Arizona and Bristol added 10.
Erin Buescher led Santa Barbara with 19 points and 10 rebounds. Stacy Clinesmith had 15 points and Christensen had 14.