In 2003, his senior year, Watson threw three no-hitters and had a 0.10 earned run average (ERA).

He won the Bob Feller Award as the top high school pitcher in Iowa.

José Ascanio was designated for assignment to make room for Watson on the Pirates' 25-man roster.

[7] Watson made his major league debut on June 8, 2011, striking out both batters he faced, Chris Young and Juan Miranda of the Arizona Diamondbacks.

On May 26, 2014, Watson got his first career big league hit, a single off of Carlos Torres of the New York Mets.

[14] In the post-season, he pitched in all three rounds of the playoffs, and was the winning pitcher in two games of the 2017 World Series.

[14] On February 19, 2018, Watson signed a two-year contract with the San Francisco Giants that included a player option for a third year.

On February 17, 2021, Watson signed a minor league contract with the Philadelphia Phillies organization that included an invitation to Spring Training.

On July 30, 2021, Watson was traded to the San Francisco Giants in exchange for Sam Selman, Ivan Armstrong, and José Marte.

[22] Watson's great-uncle, Tom Offenburger, served as an aide to Martin Luther King Jr. and the Southern Christian Leadership Conference.