Rodriguez, playing in his 12th game while appealing a 211-game suspension for his alleged use of performance-enhancing drugs, was struck with a pitch by Boston starter Ryan Dempster in the second inning, triggering a heated incident.
Dempster had thrown behind Rodriguez earlier in the at-bat, but was not ejected by home plate umpire Brian O'Nora, prompting Yankees Manager Joe Girardi to charge from the dugout and harangue the umpire.
Girardi was ejected.
The Red Sox had forged a 6-3 lead but Rodruguez smashed a solo homer in the sixth to cut the deficit and four batters later Brett Gardner put New York ahead to stay with a bases-clearing triple off reliever Drake Britton.
Edwin Nunez went 3-for-3 with an RBI as New York racked up 17 hits and took the rubber match of a three-game series.
CC Sabathia (11-10) got the win despite allowing six runs on seven hits over 5 1/3 innings and the New York bullpen fired 3 2/3 scoreless innings, capped by Mariano Rivera's 36th save.
Dempster (6-9) was roughed up for seven runs on nine hits over 5 1/3 innings.
Swim Week Miami Beach 2014 [PHOTOS]