On May 28, 2015, Rodríguez earned the win in his MLB debut, tossing ​7 ²⁄₃ shutout innings in Boston's 5–1 victory over the Texas Rangers at Globe Life Park.
Rodríguez allowed just three hits and walked two batters, while striking out seven on 105 pitches, 68 of them for strikes.
Already the youngest Red Sox pitcher to make his debut on the road since 21-year-old Roger Clemens faced the Cleveland Indians in 1984, Rodríguez also became the youngest Red Sox starter to win his debut on the road since Billy Rohr in 1967.

His next two starts were on June 3, when he pitched seven innings giving up just one run, and June 9, when he pitched six scoreless innings.
Rodríguez became first pitcher since the advent of ERA as an official statistic in 1912 to have begun his major league career with three starts of at least six innings with one or zero earned runs allowed and at least seven strikeouts.

Overall, with the 2015 Red Sox, Rodríguez appeared in 21 games (all starts), compiling a 10–6 record with 3.85 ERA, while striking out 98 and walking 37 in ​121 ²⁄₃ innings pitched.
On May 28, 2015, Rodríguez earned the win in his MLB debut, tossing ​7 ²⁄₃ shutout innings in Boston's 5–1 victory over the Texas Rangers at Globe Life Park. Rodríguez allowed just three hits and walked two batters, while striking out seven on 105 pitches, 68 of them for strikes. Already the youngest Red Sox pitcher to make his debut on the road since 21-year-old Roger Clemens faced the Cleveland Indians in 1984, Rodríguez also became the youngest Red Sox starter to win his debut on the road since Billy Rohr in 1967.
His next two starts were on June 3, when he pitched seven innings giving up just one run, and June 9, when he pitched six scoreless innings. Rodríguez became first pitcher since the advent of ERA as an official statistic in 1912 to have begun his major league career with three starts of at least six innings with one or zero earned runs allowed and at least seven strikeouts.
Overall, with the 2015 Red Sox, Rodríguez appeared in 21 games (all starts), compiling a 10–6 record with 3.85 ERA, while striking out 98 and walking 37 in ​121 ²⁄₃ innings pitched.
Eduardo Rodríguez (left-handed pitcher)