Knudson was drafted by the Houston Astros in the third round of the 1982 amateur draft out of Colorado State University. He made his debut with the club on July 8, 1985, and took a 7–4 loss to the Philadelphia Phillies. He won his first major league game on July 10 of the following season, also against the Phillies. On August 15, 1986, he and fellow pitcher Don August were traded to the Milwaukee Brewers for pitcher Danny Darwin.