Marty Barrett was born in Arcadia, California. He is an alumnus of Arizona State University, and is the brother of Tommy Barrett, another former MLB player who played for the Philadelphia Phillies.  Marty played in the longest professional baseball game in history in 1981, a minor league game between the Pawtucket Red Sox and the Rochester Red Wings. Barrett had the distinction of scoring the winning run for Pawtucket in the bottom of the 33rd inning.

An excellent second baseman with an above-average arm, Barrett was known as a smart player and a great contact hitter, striking out only 209 times in 3378 at-bats, and collecting a significant number of big hits by driving tough pitches to the opposite field. He often was used as a specialist in bunting situations, leading the American League in sacrifice hits for three consecutive years (1986–88).  In a ten-year career Barrett was a .278 hitter with 18 home runs and 314 RBI in 941 games. Barrett successfully pulled off the hidden ball trick three times, including twice in July, 1985.

In 1981 Barrett scored the winning run in the longest game in professional baseball history, as a player for the Pawtucket Red Sox, the Class AAA affiliate of the Boston Red Sox. Barrett was driven in by Dave Koza in the 33rd inning.  In 1984 Barrett batted a career-high .303 in his first full season. But his most productive year was 1986, when he posted career-highs in RBI (60), hits (179), doubles (39), triples (4), stolen bases (15) and games played (158).  Barrett starred in 1986, when he set a major league record with 24 hits in 14 postseason games, and was named the ALCS Most Valuable Player.  In the 1986 World Series Barrett had 13 hits in 30 at bats (.433 BA), and posted an on-base percentage of .514 against the New York Mets. Near the conclusion of Game 6, he had been selected by the NBC Television broadcast team as the Player of the Game. He was the final batter in the 1986 World Series, striking out against Mets closer, Jesse Orosco. During the final game of the 1990 ALCS, Red Sox pitcher, Roger Clemens, was ejected in the bottom of the second inning. Barrett protested the call by heaving plastic water containers onto the field, and also was thrown out of the game.

Barrett held the starting second baseman position with the Red Sox for most of the 1980s. On June 4, 1989, he suffered a serious knee injury while tripping over first base following a ground out. Jody Reed took over as the starter, and Barrett played only sporadically following his recovery; he was released the following season.