Brown finished with 16 points and six rebounds while Powell had 22 points, 11 rebounds and six assists for Stanford. He controlled the paint in the first half when the Cardinal built an 18-point lead and went 11 of 14 from the free throw line.
Chasson Randle added 19 points for the Cardinal (15-7, 6-4 Pac-12), who have won three of the last four in this series between the two Bay Area rivals.
Justin Cobbs had 24 points and five rebounds for California (15-8, 6-4), which sputtered offensively in its first game since upsetting then-No. 1 Arizona last week. Tyrone Wallace added 21 points and four rebounds.
The Golden Bears were within 52-47 with 13 minutes left when Brown took over for Stanford.
He made an 18-foot jumper as part of an 8-0 run then added two free throws to make it 64-51. Cobbs stopped the run with a three-point play and later added a free throw to make it 62-51 but Brown scored nine of the next 11 points for the Cardinal and Stanford took advantage of multiple turnovers by Cal down the stretch.
It marked a rare conference road win for Stanford, which lost to the Bears 69-62 on Jan. 2. The Cardinal are 3-2 in the Pac-12 away from Maples Pavilion this season and only 15-34 since 2008-09.
They handed the Bears just their second home loss this season and moved into a tie with Cal for third place in the conference.
A week after losing to Arizona 60-57, Stanford controlled most of the first half and led by as much as 18 before the Bears made a late run to close out the half.
Powell provided the bulk of the offense, scoring nine points as part of a 15-4 run. Stanford's second-leading scorer also had one of six 3-pointers by the Cardinal in the first 20 minutes.
Cal sputtered offensively until the final 6:30 when Cobbs sparked the Bears' best run of the game.
He made two free throws, scored on a putback following a miss by teammate Jordan Mathews, added a fast-break layup then made a buzzer-beating 3-pointer to cut Stanford's lead to 42-36.
David Kravish's short hook shot pulled Cal within 52-47 early in the second half but the Bears committed turnovers on back-to-back possessions and went scoreless for the next four minutes.
Josh Huestis's runner in the lane sparked an 8-0 run and Brown's three-point play made it 69-52.