Browning connected with Dante Pettis for scores of 5, 34 and 15 yards in the second half as the Huskies (5-0, 2-0 Pac-12) pulled away after leading just 7-0 at the half.
Myles Gaskin added a 32-yard touchdown run in the third quarter and finished with 113 yards on 15 carries
Browning was 26 of 34 for 293 yards with an interception on a tipped pass. Pettis had a career-high 12 receptions for 105 yards, and his three touchdowns matched his career best.
Washington rolled up a season-high 506 total yards and the defense was equally impressive as it allowed Oregon State (1-4, 0-2) to cross midfield only once until they scored on Thomas Tyner's 15-yard run late in the fourth quarter.
Of Oregon State's first 11 possessions, eight ended with punts, two with fumbles and another with a kneel-down to end the first half. The Beavers' deepest penetration was the Washington 45 until they went 74 yards on their final possession to finish with 184 total yards.
Darell Garretson was 11-of-22 passing for 74 yards in his first start of the season. Tyner was Oregon State' leading rusher with 54 yards on nine carries.
Oregon State has been outscored 149-49 in the second half this season.
After giving up a long touchdown drive to start the game, Oregon State's defense denied Washington the rest of the first half to trail 7-0 in a battle of field position.
Browning drove the Huskies 98 yards in 10 plays on their first possession, capped by his 11-yard touchdown scramble. He hit four of his first five passes, including a 40-yard strike to Quinten Pounds.
Washington squandered its next scoring opportunity when kicker Tristan Vizcaino banged a 42-yard field goal attempt off the left upright with 2:52 left in the second quarter. The Huskies' other three possessions ended with punts.
Browning was 13 of 18 for 144 yards but sacked three times by the Beavers' blitzing linebackers, who had him running for his life several more times. Washington was held to 50 rushing yards on 18 carries.
Oregon State had just 65 total yards in the first half as it punted on all five possessions. However, punter Nick Porebski was the Beavers' best weapon with a 46.8-yard average. He denied Washington's Dante Pettis any chance to add to his NCAA record-tying eight punt returns for touchdowns.
NOTES: WR Chico McClatcher is out for the season for the Huskies after breaking his left ankle in a win at Colorado last week. McClatcher had 10 catches for 128 yards in three games. ... QB Darell Garretson made his first start this season for Oregon State in place of injured Jake Luton, a junior transfer from Ventura Community College who injured his back two weeks ago in a loss at Washington State. Garretson, a senior, started the first six games in 2016.