Iannetta's solo shot in the third inning stood as the Angels' only run until the 13th, when Josh Hamilton began a rally with a one-out walk off J.J. Hoover (0-1).
Hamilton went to second on an out, Howie Kendrick was intentionally walked and pinch-hitter Hank Conger was hit by a pitch to load the bases.
Iannetta followed with a scorcher past diving third baseman Todd Frazier, scoring Hamilton and Kendrick with the go-ahead runs.
Reds starter Johnny Cueto also was sharp, surrendering just one run on three hits over seven innings.
Cincinnati was hit by a significant injury when outfielder Ryan Ludwick dislocated a shoulder while diving into third base in the third inning.
The team said he would undergo a magnetic resonance imaging exam Tuesday.
Celebrity Families of 2014 [PHOTOS]