Morrow (3-4) broke a personal five-game winless streak, logging his first victory since May 15. The right-hander threw 6 2/3 scoreless frames, allowing five hits and one walk while fanning six.
Jose Molina went 2-for-3 with a solo homer and Jose Bautista contributed an RBI single among his two hits for Toronto.
Cincinnati's Edinson Volquez (4-3) was touched for four runs on seven hits over five frames, walking two and striking out eight.
The Reds fell to 0-5 in interleague play with the loss.
Celebrity Families of 2014 [PHOTOS]