It was the only Indianapolis score of the second half of the exhibition game and came after Cincinnati had taken a 16-14 lead on the third of Mike Nugent's three field goals.
Harnish guided the Colts 73 yards to the winning score and finished with a 9-of-16 performance for 162 yards.
Indianapolis starting quarterback Andrew Luck threw only two passes on the Colts' opening possession.
Both clubs finished the preseason at 2-2. The Colts will start up with a trip to Chicago and Cincinnati will open in Baltimore.
Notable deaths of 2014 [PHOTOS]