Barner found the end zone three times on the ground, running for 195 yards on 21 carries.
He also notched a score among his three receptions for 37 yards as the Ducks (5-0, 2-0 Pac-12) rolled to their second straight conference victory.
Marcus Mariota went 21-of-32 through the air for 169 yards, one touchdown and two interceptions for Oregon.
Washington State's Connor Halliday amassed 348 yards with a touchdown and an interception on 33-for-60 efficiency for the Cougars (2-3, 0-2).
Twelve of his completions went to Marquess Wilson for 182 yards.
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