Rodriguez's 45th homer of the season was a two-run shot in the bottom of the first. He added a two-run double in the fourth.
Four other Yankees had one RBI each and a run scored on Josh Wilson's third-inning throwing error -- one of three errors he made in the game.
Two players had two hits for the Yankees, who have won four of five.
Winner Ian Kennedy (1-0), in his first major league start, gave up three runs and five hits in seven innings, with two walks and six strikeouts.
Mariano Rivera got his 23rd save.
The loser was Edwin Jackson (4-13).
McPhee, Cokas 'working on their marriage' after affair
LGBT community has 'bullied the American people': Bachmann