A career backup with the Expos and Pirates, Goff spent his last two big league seasons with the Astros. He bat .215 with two homers in 13 games while in Houston and was probably best remembered for his final game in the majors.

On May 12, 1996, Goff homered off Ugueth Urbina of the Expos in a 7-6 loss, singled, drove in two runs and made a tag at the plate to keep a run from scoring but was released by the Astros the next day. It might have been because he also tied a major league record by allowing six passed balls that night.

For his career, he hit .215 with seven homers in 90 games.