[5] After an injury to Boston relief pitcher Joel Hanrahan in April 2013, the Red Sox called Wright up to the major leagues.

[6] Wright's first major league experience was against the Indians, the team that traded him in 2012, but he saw no action in the three-game series.

On April 23, 2013, Wright was called into a game versus the Oakland Athletics to relieve Alfredo Aceves.

[10] In six major league games with the Red Sox, Wright made one start, going 0–1 with a 2.57 ERA in 21 innings pitched.

[11] Later that morning, Wright was optioned to Triple-A Pawtucket to make room for the returning Joe Kelly.

On May 8, 2016, Wright pitched a complete game for the first time in his MLB career as the Red Sox won 5–1 over the Yankees.

On March 23, 2018, MLB announced that Wright would be suspended for 15 games for violating the league's personal conduct policy.

[18] Wright was sent on a rehabilitation assignment with Triple-A Pawtucket on August 28,[19] and returned from the disabled list on September 1.

[21] Initially included on Boston's postseason roster,[22] Wright was removed and replaced by Heath Hembree for the ALDS and beyond due to his previous knee injury.

[25] On March 6, 2019, Wright received an 80-game suspension without pay after testing positive for Growth Hormone Releasing Peptide 2 (GHRP-2), a performance-enhancing substance, in violation of MLB’s Joint Drug Prevention and Treatment Program.

Wright was released by the Red Sox on October 18,[31] and he announced shortly thereafter that he would undergo Tommy John surgery.

[32] On March 21, 2021, Wright signed a minor league contract with the Pittsburgh Pirates that included an invitation to spring training.