Casey surpassed OSU's Jack Riley, who won 613 games at OSU from 1973-1994. Casey, now in his 18th season with the Beavers, has averaged 34 wins a season with the Beavers.
The win moved Casey into 13th place in Pac-12 history for most wins.
"It's great to do it the way we won it," Casey said. "I have so much respect for this program and people who came before me. I feel honored and blessed to be the head coach at Oregon State."
Barnes, who went 3-for-5, snapped a 3-3 tie with a two-out, two-run single in the fifth. OSU had tied the game a batter earlier when Ryan Dunn walked with the bases loaded on a 3-2 count.
Barnes added to the OSU (36-18 overall, 16-12 Pac-12 Conference) lead with a run-scoring single in the seventh, the first of two runs for the Beavers in the inning as Joey Matthews was hit by a pitch with the bases loaded for the 7-3 advantage.
Tyler Smith and Kavin Keyes had two apiece in the win.
Ben Wetzler started for the Beavers and calmed down after a 35-pitch first inning. He went 5 2/3 innings, throwing 111 pitches to pick up the win and improve to 7-2 this season. He allowed eight hits and three runs while striking out six and walking four against Oregon (42-15, 19-9).
Scott Schultz worked the final 3 1/3 innings for the Beavers, allowing only a baserunner in the ninth on a hit batter. He struck out three to get his first save of the season.
Oregon State and Oregon continue their series Saturday with a 1:05 p.m. PT first pitch at Goss Stadium.
Saturday's 1:05 p.m. start will be the fourth home television broadcast for the Beavers this season. Fans in the Eugene/Corvallis region can find the game live on KEZI 9.2 over the air (channel 309 digitally).
Those throughout the rest of the Pacific Northwest can watch the game on ROOT Sports.
Fans across the nation can also catch the action on Fox College Sports Pacific (FCS Pacific, channel 415 on Comcast).
The broadcast will also be streamed on Beaver Nation Online (osubeavers.com) for a fee.