The senior running back, whom the Beavers will depend on this season since they have a still-learning freshman quarterback, ran for 151 yards and a touchdown in Oregon State's 35-21 victory last weekend against San Jose State.
The breakout came after he sat out of the first half of the Beavers' previous game, a 35-7 loss at Michigan, because of a lingering knee injury.
But he'll face a bigger challenge this Friday night when Oregon State (2-1) hosts No. 21 Stanford (2-1).
''We've got to just focus up,'' Barrs-Woods said. ''That's what it comes down to. We've got to focus up. We can't get penalties against them, we can't beat ourselves against them.''
The Cardinal are coming off a 41-31 upset victory over USC last Saturday in Los Angeles, which popped Stanford back into the AP rankings at No. 21. In that game, Stanford limited the Trojans to 155 total yards on the ground.
Through three games this season, Stanford has allowed opponents an average of 139.7 total rushing yards and just two total touchdowns on the ground.
The Cardinal also have a history of success in stopping Oregon State's rush. Last year, in a 38-14 rout in Palo Alto, Stanford held the Beavers to just 12 yards on the ground.
Since 2009, Oregon State has not managed to clear 100 yards rushing in games against the Cardinal.
The Beavers know now would be a good time to change that, but the young team is still very much a work in progress.
''We still have a ways to go in the run game,'' coach Gary Andersen said. ''Last week, we ran the ball effectively. One place we need to improve on is when we get into those third-and-2, third-and-1 situations. There's been a couple times where we have not been able to produce in those situations and we'll continually work at that.''
Against San Jose State, Barrs-Woods had the second-best rushing performance of his career and the Beavers totaled 305 yards on the ground, the first time they've gone over the 300-yard mark since 2008. Quarterback Seth Collins added 114 rushing yards.
It was just the 15th time in school history that two or more Beavers have each surpassed the 100-yard mark in a single game.
Barrs-Woods put to rest any lingering concern about his knee when he broke free for a 38-yard dash in the third quarter.
''Storm always runs hard when he's ready to go and I thought he had some good, physical runs,'' Andersen said. ''It was just good to see him out there. It brought a smile to my face to see him break some tackles.''
Barrs-Woods, who hails from Pflugerville, Texas, had his best season in 2012 when he ran for 940 yards and 13 touchdowns. He's struggled at times since then because of different injuries.
But, with 2,410 career rushing yards, he's within striking distance of fifth place on Oregon State's career rushing list - behind Beavers stars Kenny Simonton, Jacquizz Rodgers, Steven Jackson and Yvenson Bernard. Pretty solid company.
Collins, who got his first good look at Barrs-Woods in action, was impressed with his pre-game roommate.
''I expect nothing but greatness out of Storm,'' he said.
AP college football site: www.collegefootball.ap.org