Guzmán was signed by the Texas Rangers as an amateur free agent on February 10, 1981. He made his major league debut on September 10, 1985 against the Oakland Athletics. He remained with the Rangers for six seasons winning the 1991 MLB Comeback Player of the Year Award after improving from an 11–13 season to 13–7 in 1991.\n', '

In December, 1992, Guzmán signed as a free agent with the Chicago Cubs. On April 6, 1993, in defeating the Atlanta Braves 1–0 at Wrigley Field, Guzmán had a no-hitter broken up by an Otis Nixon single with two out in the ninth—the only hit he would allow. The no-hitter would have been the first pitched by a Cub (and, in fact, the first the Cubs had been involved in) since Milt Pappas in 1972.\n', '

He remained with the Cubs for one more season pitching his final game on May 23, 1994.\n', '

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