Smith caught eight passes for 140 yards, helping the Colts win for the first time in the pre-season.
Collins was 5-of-10 for 45 yards and played into the second quarter.
Andy Dalton played the first two series for the Bengals and was 6-of-9 for 43 yards. Bruce Gradkowski came in to complete 14-of-17 for 90 yards.
After Smith's winning touchdown pass, the Bengals drove deep into Colts territory before Kevin Thomas came up with an interception.
Cincinnati, which went 1-3 in the pre-season, opens next week at Cleveland.
Swim Week Miami Beach 2014 [PHOTOS]