Rodriguez gave up nine earned runs in his last start, but he had little trouble with the Royals, whose four-game winning streak ended. Rodriguez gave up six hits, walked one and struck out five.
Mookie Betts had four hits for Boston, Blake Swihart had two hits and two RBIs and Hanley Ramirez belted his 14th homer.
Right-hander Yohan Pino got an emergency start for the Royals, filling in for the injured Yordano Ventura. Pino struggled, giving up 11 hits and six runs over 5 1/3 innings. He didn't strike out a batter.