The touchdown by Sanu put the Bengals in front 17-13 and they added a 1-yard scoring run by Jourdan Brooks in the fourth period at the end of a 12-play, 81-yard drive directed by Zac Robinson.
Atlanta closed within five points on a 7-yard touchdown throw from Dominique Davis to LaMark Brown and a final attempt to pull out a win ran out of downs at the Bengals' 26-yard line with 9 seconds left.
Cincinnati quarterback Andy Dalton completed 8-of-15 passes for 125 yards and a touchdown in first-half action.
Atlanta's Matt Ryan was 18-of-21 for 174 yards and a touchdown while helping the Falcons to a 13-10 halftime lead.
The Bengals have won both their pre-season games and Atlanta is 0-2.