Moret was a member of the 1975 American League champion Red Sox. After winning 14 of 17 decisions during the regular season in 36 games (including 16 starts), he appeared in four postseason contests. In the ALCS, he was the winning pitcher in relief of Reggie Cleveland in Game 2 against the Oakland Athletics, hurling a scoreless sixth inning and earning the victory when Boston broke a 3–3 tie in their half of the frame. Then, in the 1975 World Series, Moret worked in three games, including the legendary Game 6. He held the Cincinnati Reds scoreless in 1 innings pitched, although he allowed two hits and three bases on balls, one of those intentional. He was traded to the Braves for Tom House a little more than seven weeks after the conclusion of the Fall Classic on December 12, 1975. At the time, the Braves needed more starting pitching of which the Red Sox had a surplus. Nearly one year later on December 9, 1976, Moret was part of a five-for-one trade that sent him, Ken Henderson, Dave May, Adrian Devine, Carl Morton, and $200,000 from the Braves to the Rangers for Jeff Burroughs.