After the college baseball season, the Nationals signed Peacock to a $110,000 signing bonus. He spent the 2007 season with the GCL Nationals, Washington's affiliate in the rookie-level Gulf Coast League, accruing a record of 1 win and 1 loss and a 3.89 earned run average. Over 39⅓ innings in 2007, consisting of seven starts and six appearances in relief, Peacock struck out a total of 34 batters and issued 15 bases on balls. In 2010, he made eight starts for the Harrisburg Senators of the Class AAEastern League. After the 2010 season, Peacock played in the Arizona Fall League as a relief pitcher, and his fastball was measured at. Baseball America rated Peacock the 42nd best prospect in baseball during the 2011 season. He represented the Nationals at the 2011 All-Star Futures Game. He was named a starting pitcher on Baseball America's 2011 Minor League All Star team. Peacock began the 2011 season with Harrisburg and also played for the Syracuse Chiefs of the Class AAAInternational League. He was promoted to the majors and made his MLB debut on September 6, 2011. He earned his first major league win on September 14.
After the 2012 season, the Athletics traded Peacock to the Houston Astros with Max Stassi and Chris Carter for Jed Lowrie and Fernando Rodriguez. He spent the entire season at the AAA level. Peacock began the 2013 season at the AAA level before being called up by the Astros. He pitched to a 5.18 ERA in innings. In 2014, he pitched a career high 24 starts, finishing 4-9 in innings. Peacock was out of options in 2017, and so could not be sent to the minor leagues. He began the season as a relief pitcher, with a 1.10 ERA in innings pitched, and received a spot start on May 22 in place of the injured Dallas Keuchel. Following a start in which Peacock allowed one hit and no runs in innings, Peacock replaced Mike Fiers in the starting rotation. The Astros won the American League West with 101 wins, and faced the Los Angeles Dodgers in the World Series. In Game 3, Peacock earned his first major league save by completing the final innings of a 5−3 win, allowing no hits and striking out four. It was the longest hitless relief outing since Ron Taylor's four innings in Game 4 of the 1964 World Series, and tied Ken Clay for the longest hitless postseason save, first accomplished in the 1978 American League Championship Series. The Astros would then win the 2017 World Series, their first in franchise history. In 2018, Peacock pitched the whole season out of the bullpen, totaling 61 appearances. He struck out 96 batters in 65 innings. He was 3-5 with three saves and had a 3.46 ERA. On May 8, 2019, Peacock threw a career-high 12 strikeouts in 7 innings against the Kansas City Royals. In 2019 he was 7-6 with a 4.12 ERA, and struck out 96 batters in innings.
Personal life
Peacock's father, Jerry, converted a trailer that he slept in in order to follow Brad in the minor leagues. Brad and his wife, Stephanie, had a son in June 2017.