He played in Major League Baseball (MLB) for the Seattle Mariners, Toronto Blue Jays, San Diego Padres, Los Angeles Dodgers, and Chicago Cubs.

He picked up the win in relief versus the University of California Los Angeles on April 25 going one inning, surrendering one hit, and striking out two.

Morrow was named National Pitcher of the Week after pitching seven innings, no hits, no runs, one walk and a career-high 12 strikeouts against University of California, Irvine.

He was named a third-team preseason All-American and the fifth-best professional prospect out of the Cape Cod League by Baseball America.

On April 23, he earned his first major league win against the Texas Rangers, allowing one hit in career-high three and one third innings pitched.

After missing two weeks of spring training in 2008 due to a sore shoulder,[7] Morrow was optioned to the Mariners minor league affiliate Double-A West Tennessee on March 30.

Morrow was recalled to the Seattle bullpen 17 days afterwards when Mariners starter Érik Bédard was placed on the 15-day disabled list.

[11] On March 29, 2009 the Mariners announced that Morrow would no longer be used as a starting pitcher; instead, he would move into a relief role with the organization.

[16] Morrow won his fifth consecutive decision for Tacoma tossing five scoreless innings to lead the Rainiers to a 4–1 win over the Portland Beavers on August 29.

[22][23] Despite some struggles with inconsistency during the early stages of the alterations, statistics show that his production stabilized as the season progressed and he managed to produce favorable results on a regular basis before the end of the season, including a stellar 17 strikeout, one hit performance that was a candidate for MLB.com's This Year in Baseball Performance of the Year.

[24] On August 8, Morrow was one out away from a no-hitter against the Tampa Bay Rays when Evan Longoria hit an infield single.

He made his regular-season debut on April 23 against the Tampa Bay Rays, pitching 5+1⁄3 innings, giving up 3 hits, 2 runs, 2 walks and 10 strikeouts.

For the first time since being traded, Morrow returned to the home stadium of his former team, the Seattle Mariners, to start against them on August 17.

[29] Morrow became the first pitcher in major league history to pitch 100 innings in one season without the team recording a double play behind him.

[30] On September 23, after 173+1⁄3 innings dating back to August 28, 2010, Desmond Jennings of the Tampa Bay Rays grounded into Morrow's first double play in 30 starts.

Morrow and Álvarez thus became the first Blue Jays starters to throw back-to-back shutouts since Jack Morris and Al Leiter did so on June 16 and 17, 1993.

[34] Morrow experienced "stabbing pain" during the first inning of his June 11 start while pitching to Bryce Harper, the second hitter in the Washington Nationals lineup.

On February 5, 2013, manager John Gibbons named Morrow the number 2 starter for the upcoming season, behind reigning NL Cy Young Award winner R. A.

[37] After opening the season with a 2–3 record and a 5.63 earned run average, Morrow was placed on the 15-day disabled list on June 1 with a right forearm strain.

[40] On July 24, it was reported by Rogers Sportsnet that Morrow was diagnosed with an entrapped radial nerve in his right forearm, and would likely miss the rest of the 2013 season.

[41] Blue Jays management said the following day that they expected Morrow to pitch again in 2013, either in late September or in October's instructional league in Florida.

On March 18, manager John Gibbons confirmed that Morrow would be the team's fifth starter, citing a need to give him more time to prepare for the regular season.

[44] After struggling to open the season, including a start on April 26 where he walked 8 Red Sox batters over 22⁄3 innings, Morrow was placed on the 15-day disabled list on May 3 with a sprained right index finger.

[52] On December 17, Morrow signed a minor league contract with the Padres that included an invitation to spring training.

[53] On January 25, 2017, Morrow signed a minor-league contract with the Los Angeles Dodgers that included an invitation to major league spring training.

[54] He did not make the major league team and was assigned to the Triple-A Oklahoma City Dodgers to begin the season.

On December 11, 2020, Morrow signed a minor league contract to return to the Los Angeles Dodgers organization.

[65] In September 2011, Morrow debuted a new cut fastball which came from making a slight adjustment on his slider, with velocity hovering around 88–91 mph.