Barrios was acquired from the Jalisco Charros of the Mexican League for shortstop Rudy Hernández, and played his entire major league career with the White Sox. He joined the starting rotation in 1976, and on July 28 combined with Blue Moon Odom to no-hit the Oakland Athletics, 2–1, at the Coliseum.[citation needed] His most productive season came in 1977, when he recorded career-numbers with 14 wins, 119 strikeouts, nine complete games, and 231 innings pitched. Despite his 9-15 mark in 1978, he threw two shutouts with a 3.82 ERA in a career-high 33 starts. His 1979 season ended on September 25 when he underwent rotator cuff surgery.
Barrios had a 1–3 record as a spot starter until being placed on the disabled list on June 4 because of a swollen right elbow just before the 1981 MLB strike. During the work stoppage on June 24, he was charged with one count of cocaine possession and arrested for disorderly conduct at a Division Street bar owned at the time by Doug Buffone. He voluntarily entered a Chicago area drug and alcohol rehabilitation center on July 3. He was released by the White Sox on September 1 after eight starts with a 3.96 ERA in .mw-parser-output .frac{white-space:nowrap}.mw-parser-output .frac .num,.mw-parser-output .frac .den{font-size:80%;line-height:0;vertical-align:super}.mw-parser-output .frac .den{vertical-align:sub}.mw-parser-output .sr-only{border:0;clip:rect(0,0,0,0);height:1px;margin:-1px;overflow:hidden;padding:0;position:absolute;width:1px}36+1⁄3 innings.
Barrios enjoyed a good winter season in the Mexican Pacific League and was ready to sign a contract with the Milwaukee Brewers for the 1982 season, when he died of a heart attack at the age of 28 on April 9.

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