The Yankees had taken a 2-1 lead in the fifth inning on Nick Swisher's sacrifice fly and, after Robinson Cano singled off Derek Holland (2-1), Rodriguez blasted an 0-1 pitch over the left-center field wall to break the game open.
Jeter added an RBI double and Curtis Granderson drove in two runs for New York, which notched its fourth straight win.
CC Sabathia (2-0) earned the victory, surrendering four runs on seven hits over eight innings. The left-hander issued only one walk and struck out eight.
Josh Hamilton homered for the American League West-leading Rangers, who dropped the opener of a three-game set against the Yanks.
Holland finished with seven earned runs allowed on nine hits over six frames.
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