In 40 games, and 43.1 innings, in 2013 for Arizona before being traded, he had a 2–0 record and a 2.70 ERA with 42 strikeouts, and limited opposing batters to a .233 batting average. As of the end of the 2017 season, he was the player with the most innings pitched for Arizona without ever losing. He was one of only two pitchers with a 1.000 winning percentage with Arizona who had more than one victory, with the other being Jimmie Sherfy.
In January 2013, he signed a two-year contract with the Red Sox for at least $6.25 million. He received $2.325 million in 2013, and $3.825 million in 2014. The Red Sox had a $4 million option for 2015, with a $100,000 buyout.
In the 2013 regular season, he was 5–2 with a 1.81 ERA (third among left-handed relievers in the American League), in 61 games and 59.2 innings, and held opposing batters to a .228 batting average. His 0.65 ERA the second half of the season was fourth-best among major league relievers with at least 25 innings thrown. In his last 28 appearances of the regular season, he allowed only one run.
In the 2013 American League Division Series, he pitched 3.2 scoreless innings over 3 games, notching a win and allowing two hits and one walk while striking out four, as the Red Sox defeated Tampa Bay. In the 2013 American League Championship Series, he added 3.1 scoreless innings against the Detroit Tigers, bringing his post-season total to 7 scoreless innings in 7 appearances, in which he held the opposition to a .130 batting average. Breslow wrote a blog during the 2013 post-season. During the 2013 playoffs, he pitched in 10 of 16 games, garnering a 2.45 ERA.