Peavy (3-0) allowed two walks and struck out five, raising his total to 26 over 28 2/3 innings to start the season.
The former Cy Young award winner threw 71 of his 107 pitches for strikes and lowered his ERA to 1.88 with the dominating performance in the opener of a three-game set at Oakland.
Athletics starter Bartolo Colon (3-2) yielded two runs on seven hits in a seven-innings to take the loss.
The A's lost for the third time in four games.
Boston schools pull out free condoms over wrapping complaints
NBC reportedly holds celebs hostage to Jimmy Fallon's show