Woods gained 46 yards on 17 carries and made three catches for 20 yards as the Beavers (6-0, 4-0 Pac-12) continued their best start since 1907.
Cody Vaz picked up 174 yards on 16-of-26 passing efficiency while Oregon State's defense forced a pair of fumbles and picked off two Utah passes.
Markus Wheaton led the Beavers' receiving corps with seven grabs for 90 yards.
The Utes (2-5, 0-4) dropped their fourth straight as Travis Wilson was held to 15-for-27 passing for 172 yards with a touchdown and two interceptions.
2014: The Year in Music [PHOTOS]