On July 20, 2012, Musgrove was traded from the Blue Jays to the Houston Astros with Francisco Cordero, Ben Francisco, Asher Wojciechowski, David Rollins, Carlos Pérez and a player to be named later in exchange for J. A. Happ, Brandon Lyon, and David Carpenter. After the trade, Musgrove was assigned to the Greeneville Astros. In 17 total innings pitched between Bluefield and Greeneville, he was 0-1 with a 4.24 ERA. He spent 2013 with the Gulf Coast Astros where he pitched to a 1-3 record and 4.41 ERA in 11 games, and 2014 with the Tri-City ValleyCats, where he compiled a 7-1 record and 2.81 ERA in 15 games. Musgrove started 2015 with the Quad Cities River Bandits and was promoted to the Lancaster JetHawks and Corpus Christi Hooks throughout the season. In 19 games between the three clubs, Musgrove was 12-1 with a 1.88 ERA. The Astros added him to their 40-man roster after the season. He began 2016 with Corpus Christi and was promoted to the Fresno Grizzlies in May. Musgrove was recalled by the Astros from Fresno on August 1, 2016. In 16 games between Corpus Christi and Fresno prior to his promotion, he was 7-4 with a 2.74 ERA. He made his major league debut on August 2 versus the Toronto Blue Jays, striking out eight over 4.1 innings while only allowing one hit. His first Major League strikeout victim was Edwin Encarnación. He spent the remainder of the season with the Astros, going 4-4 with a 4.06 ERA over 11 games. Musgrove began 2017 with Houston, and spent the majority of the season there, pitching only one game with Fresno. In 38 games for the Astros in 2017, he was 7-8 with a 4.77 ERA. In the postseason, he appeared in seven games, including four World Series games. In four innings pitched, he allowed three hits and three runs, but threw a scoreless top of the 10th inning of Game 5 against the Dodgers where he was the winning pitcher. The series concluded after 7 games with the Astros winning the title. Three years later, it was revealed in the Houston Astros sign stealing scandal that the Astros had cheated during the 2017 season. Musgrove subsequently said he thought the team's championship was "tainted" because of this.
Pittsburgh Pirates
On January 13, 2018, the Astros traded Musgrove, along with Michael Feliz, Colin Moran and Jason Martin, to the Pittsburgh Pirates for Gerrit Cole. He began the season on the disabled list and was activated on May 25, joining the starting rotation. Pitching against the St. Louis Cardinals on August 30, 2018, Musgrove began the game by throwing 21 consecutive strikes, the most by a major league pitcher to start a game since 1988. This included eight swinging strikes, six called strikes, two foul balls and five balls in play where the batter was put out by the Pirates fielders. In 19 starts, he finished with a record of 6-9 in innings. In 2019, his left-on-base percentage of 63.2% was the worst in the majors.
