Morgan made his major league debut on June 11, throwing a complete game in a 3–0 loss to Scott McGregor and the Baltimore Orioles.

[4] After losing his first three starts in Oakland, Morgan was sent down to AAA Vancouver for the rest of the season, going 5–6 with a 5.58 earned run average (ERA) in 92 innings pitched.

After starting the 1979 season with the AAA Ogden A's, Morgan was called up again to the big club after posting a 5–5 record with a 3.48 ERA in 101 innings.

After finishing another unspectacular season in 1980, going 6-9 back at Ogden, Oakland traded Morgan on November 3 to the New York Yankees for 33-year-old infielder, Fred Stanley.

After losing much of 1985 to arm trouble, Morgan spent most of the next three seasons pitching for Seattle and compiling similar numbers to his career average, going 24–35 with a 4.53 over 429 innings with 216 strikeouts and 144 walks.

He also went to the post-season for the first time, relieving in two games without giving up a run, but the Cubs lost to the Atlanta Braves in the National League Division Series.

Prior to spring training in 2000, the 40-year-old signed with his 12th team, the Arizona Diamondbacks, who successfully converted Morgan to a full-time reliever.

Morgan excelled in this new role and appeared in 60 games, pitched 100 innings, and compiled an ERA that was only slightly above career average.

He came back to make the final appearance of his career on September 2, pitching 1+1⁄3 innings and giving up an unearned run in a 19–1 loss to the Dodgers.

Morgan was the last active player to have competed during the 1978 season and one of the last four (the others being Jesse Orosco, Rickey Henderson and Tim Raines) to have debuted in the 1970s.

Morgan was tied with National Hockey League player Mike Sillinger and MLB pitcher Matt Skrmetta for the most teams played for in any North American professional sport through June 2006, when Skrmetta signed with the Chicago White Sox, his 24th professional team and 13th organization.