Schaub, who completed 11 of 13 passes for 115 yards, gave the Falcons a 20-14 lead with 10 seconds remaining in the half. He tossed a 3-yard pass to Fred McCrary, who bobbled the ball on the 1 and then rolled into the end zone before being touched.
Jason Wright increased the Falcons' lead to 27-14 when he ran in from the 1-yard line with just more than six minutes remaining at Tokyo Dome.
With 4:02 left, the Colts cut the lead to 27-21 on a 3-yard touchdown pass from Travis Brown to John Standeford. A 45-yard pass from Brown to Montiese Culton set up the final touchdown.
The game featured two of the NFL's marquee quarterbacks in Peyton Manning and Michael Vick.
Manning threw a 2-yard touchdown pass to Troy Walters at 6:45 of the first quarter, giving the Colts a 7-0 lead. Todd Peterson's two field goals made it 7-6.
Vick came out after the first play of the second quarter. Manning came out with just more than nine minutes left in the second quarter.
Vick completed 4 of 7 passes in the first quarter for 51 yards; Manning was 6 for 8 for 36 yards with one interception.
Indianapolis running back Edgerrin James carried the ball three times for 20 yards. His longest carry was 9 yards.
The Colts took a 14-6 lead with 7:48 remaining in the second quarter when linebacker Kendyll Pope scored after picking up a loose ball that resulted from a botched handoff from Schaub to Wright inside the Atlanta 5.
Atlanta drew to 14-13 with three minutes left in the first half on a 6-yard touchdown pass from Schaub to Brian Finneran.
The NFL's series of international games began in 1986 in response to growing interest in American football around the world. Since then, 39 games have been played in 12 cities outside the United States. Tokyo has hosted 13 American Bowl games.