The Angels selected him in the sixth round of the 2007 Major League Baseball draft. From 2007 through 2013, Brasier pitched for various Angels farm teams, starting with the Rookie LeagueOrem Owlz and reaching the Triple-ASalt Lake Bees. He made a career-high 55 appearances with the Bees in 2012, recording 13 saves along with a 7–3 record, 54 strikeouts, and 24 walks in innings pitched. The Angels promoted Brasier to the major leagues for the first time on May 1, 2013. He made his MLB debut the next day, pitching an inning of relief against the Baltimore Orioles, allowing two runs on two hits. After making one additional appearance in May, he returned to the minors and was recalled in September when the major league rosters expanded; he made five appearances during the month. Overall, with the 2013 Angels, Brasier made seven appearances, striking out seven and walking four in nine innings pitched with a 2.00 ERA. Brasier was outrighted off of the Angels 40-man roster on October 28, 2014.
On July 7, 2015, Brasier signed a minor league deal with the Oakland Athletics. He spent 2015 and 2016 in Oakland's farm system, including 46 relief appearances with the Triple-A Nashville Sounds in 2016, recording a 3.56 ERA in innings.
Hiroshima Toyo Carp
The Athletics sold his contract to the Hiroshima Toyo Carp of Nippon Professional Baseball on December 14, 2016. With the Carp in 2017, Brasier made 26 relief appearances; in 30 innings of work he struck out 19, walked eight, and had a 3.00 ERA.
On March 4, 2018, Brasier signed a minor-league contract with the Boston Red Sox. Pitching for the Pawtucket Red Sox of the Triple-A International League, he was selected to appear in the Triple-A All-Star Game. The Red Sox promoted Brasier to the major leagues on July 8; he made his Boston debut the next day, pitching one inning against the Texas Rangers and retiring the side in order. On August 30, Brasier recorded his first MLB win, pitching an inning of scoreless relief in a come-from-behind victory over the Chicago White Sox. Brasier proved to be a consistent reliever down the stretch, finishing with a 1.60 ERA in 34 appearances, and was the recipient of the Red Sox' Lou Gorman Award. Brasier was included on Boston's postseason roster, making a total of nine appearances and allowing one earned run in innings, as Boston went on to win the World Series. Brasier was included on Boston's Opening Day roster to start the 2019 season. On April 3, Brasier recorded his first major league save in closing out a 6–3 win over the Athletics. He was placed on the bereavement/family medical emergency list on June 11, and re-activated on June 17. Brasier was optioned to Pawtucket on July 16, and recalled to Boston on August 17. Overall with the 2019 Red Sox, Brasier appeared in 62 games, compiling a 2–4 record with seven saves, along with a 4.85 ERA and 61 strikeouts in innings.
