Clemens, 44, had a 1-3 record and a 5.32 earned run average in his four prior starts. Clemens (2-3) retired the last 15 batters he faced, giving up one run on two hits with four strikeouts and one walk. The Twins didn't have a base runner with Clemens on the mound after Joe Mauer's leadoff double in the fourth.
Clemens became the eighth pitcher with at least 350 wins and the first since Warren Spahn in 1963.
Boof Bonser (5-5) matched Clemens for five innings. In the sixth, Bobby Abreu homered and Bonser allowed two more hits before leaving. He was charged with four runs on nine hits with six strikeouts and three walks over 5 1/3 innings.
Abreu had three hits, including his fifth home run of the season, and Derek Jeter drove in two runs. Alex Rodriguez was 0-for-4 with two strikeouts before leaving the game in the bottom of the sixth with a leg injury.