Detroit Tigers Minor leagues Alexander signed with the Tigers and spent the 2015 season with the
Connecticut Tigers, posting an 0–2 record and 0.97 ERA in 37 innings pitched. He started 2016 with the
Lakeland Flying Tigers and was promoted to the
Erie SeaWolves during the season. In 25 total games (24 starts) between the two teams, he pitched to an 8–8 record and 2.44 ERA with a 1.05 WHIP. He returned to Erie in 2017, posting an 8–9 record, a 5.07 ERA, and 120 strikeouts in 27 games (26 starts), and in 2018, he played for both Erie and the
Toledo Mud Hens, going 6–8 with a 4.44 ERA in 26 games (24 starts).
Major leagues Alexander returned to Toledo to begin the 2019 season. On July 3, 2019, the Tigers selected Alexander's contract and promoted him to the major leagues as the 26th man of a doubleheader against the
Chicago White Sox. In his major league debut, he pitched five innings, allowing two runs and recording four strikeouts (including the very first batter he faced). On September 16, Alexander pitched six innings of one-run baseball against the
Baltimore Orioles, earning his first major league win. On August 2, 2020, against the
Cincinnati Reds, Alexander set an MLB record for a reliever by striking out nine consecutive batters. He also tied the American League and Tigers' franchise record of nine consecutive strikeouts set by
Doug Fister on September 27, 2012. He became the first pitcher with 10 or more strikeouts in a relief outing since
Randy Johnson set the strikeout record for a relief pitcher with 16 on July 18, 2001. (Johnson's record was accomplished on the second day of a suspended game; while he was the first pitcher to appear that day, he was officially listed as a reliever.) With the
2020 Detroit Tigers, Alexander appeared in 14 games, compiling a 2–3 record with a 3.96 ERA and 34 strikeouts in innings pitched. Alexander made the Tigers
Opening Day roster out of 2021 spring training. He began the season as a long reliever and occasional "opener" (pitching the first two to three innings of a game), before being moved to an official starting role in July. On August 20, Alexander pitched a career-high seven innings and allowed only one run against the
Toronto Blue Jays to record his first
quality start of the season. Overall in 2021, Alexander appeared in 41 games (15 starts), posting a 2–4 record and 3.81 ERA, while striking out 87 batters in innings. Alexander made the Tigers'
Opening Day roster out of 2022 spring training. He suffered a left elbow sprain and was placed on Detroit's 15-day IL on May 2, retroactive to April 30. He was recalled to the Tigers on June 14. On September 19, Alexander took a no-hitter into the seventh inning against the
Baltimore Orioles before surrendering a leadoff single to
Ryan Mountcastle. Alexander ended up throwing seven shutout innings as he and the Tigers won 11–0. On November 18, Alexander signed a one-year, $1.875 million contract with the Tigers, avoiding arbitration. Alexander began the 2023 season mainly pitching out of Detroit's
bullpen. He made 25 appearances, recording a 4.50 ERA with 44 strikeouts in 44.0 innings of work before he was placed on the 60-day injured list with a
lat strain on July 4, 2023. Following the season on November 6, Alexander was
designated for assignment by the Tigers.
Tampa Bay Rays On November 10, 2023, Alexander was claimed off waivers by the
Tampa Bay Rays. On May 17, 2024, he threw
perfect innings vs. the
Toronto Blue Jays before giving up a single, a home run, and another single and being pulled. This was the 2nd longest perfect game bid in Rays history, behind the duo of
Ryne Stanek and
Ryan Yarbrough in 2019 and
Drew Rasmussen in 2022, both 8 innings against the
Baltimore Orioles. In 23 games (9 starts) for Tampa Bay, he compiled a 6–5 record and 5.10 ERA with 90 strikeouts across innings pitched. On November 22, the Rays non–tendered Alexander, making him a free agent.
Milwaukee Brewers On February 12, 2025, Alexander signed a one-year contract with the
Milwaukee Brewers. In 21 appearances (four starts) for Milwaukee, he struggled to a 3–5 record and 6.19 ERA with 30 strikeouts across innings pitched. On June 1, Alexander was designated for assignment by the Brewers. He elected free agency in lieu of an outright assignment to the Triple-A
Nashville Sounds on June 6.
Chicago White Sox On June 8, 2025, Alexander signed a minimum-salary, major league contract with the
Chicago White Sox. He made 31 appearances (one start) for Chicago, registering a 2–9 record and 4.26 ERA with 52 strikeouts across innings pitched.
Texas Rangers On December 15, 2025, Alexander signed a one-year, $1.125 million contract with the
Texas Rangers. ==Pitch selection==