After cups of coffee with the Indians in the late 1970s, Griffin got his first chance at a starting job when Cleveland traded him to Toronto in December 1978. Griffin’s .080 batting average to start the season nearly prompted his demotion, but as soon as manager Roy Hartsfield warned him that he was in danger of losing his job the rookie shortstop reeled off a 19-game hitting streak. By the end of the season he had been named co-winner of the 1979 AL Rookie of the Year award along with Minnesota’s John Castino.
All the same, Griffin was valued far more for his glove than his bat. Mike Scioscia called him “the Ozzie Smith of the American League.” A steady, everyday shortstop, he spent six years with the Blue Jays, playing in 392 consecutive games. He was traded after the 1984 season to Oakland, where, despite his reluctance to draw walks and a tendency to be overaggressive on the basepaths, he began to harness the offensive promise he showed in 1980 when he set an AL record for most triples by a switch-hitter with a league-leading 15.
After establishing personal bests in most offensive categories with the Athletics, Griffin was traded to the Dodgers for Bob Welch prior to the 1988 season in a move that helped both teams to league championships. A Dwight Gooden fastball broke his hand in May 1988, and he was disabled for much of 1988 and part of 1989.
Griffin returned to Toronto in 1992 and was a key contributor as the Jays took the first of two consecutive championships. On October 13, 1993, he stood on deck as Joe Carter faced Mitch Williams in the ninth inning of Game Six. His career came to an end minutes later when Carter homered to win the World Series for Toronto.