[3] From 2007 through 2013, Brasier pitched for various Angels farm teams, starting with the Rookie League Orem Owlz and reaching the Triple-A Salt Lake Bees.

[5] He made his MLB debut the next day, pitching an inning of relief against the Baltimore Orioles, allowing two runs on two hits.

[9] Brasier missed the entire 2014 season after undergoing Tommy John surgery[10] and was outrighted off of the Angels 40-man roster on October 28, 2014.

[4] Brasier was invited to major league spring training by the Athletics in 2017 but took the opportunity to make more money overseas and agreed to have his contract sold to the Hiroshima Toyo Carp of Nippon Professional Baseball on December 14, 2016.

[15] The Red Sox promoted him to the major leagues on July 8[16] and he made his Boston debut the next day, pitching one inning against the Texas Rangers and retiring the side in order.

[17] 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.

[18] He 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.

[20] Brasier was included on Boston's Opening Day roster to start the 2019 season[21] and on April 3, he recorded his first major league save in closing out a win over the Athletics.

[29] Overall during the 2021 regular season, he made 13 appearances with Boston, all in relief, compiling a 1.50 ERA and 1–1 record while striking out nine batters in 12 innings.

[24] On May 14, Brasier was designated for assignment by Boston, hours after he allowed three runs in a relief appearance against the St. Louis Cardinals at Fenway Park.

[36] He made two scoreless appearances for the Triple-A Oklahoma City Dodgers before he was selected to the major league roster on June 20.