Knapke, a redshirt sophomore making his second career start, set school records for attempts (73) and completed passes (46) as he threw for 395 yards and three touchdowns. Lewis, a freshman, finished with 16 receptions for 140 yards and a touchdown for Bowling Green (2-1).
Indiana took a 42-39 lead with 2:04 remaining on a 1-yard run by quarterback Nate Sudfeld on a fourth down play.
The Falcons then moved 88 yards in 12 plays for the winning score. The PAT was blocked after the Falcons' touchdown. Indiana had one final chance, but Bowling Green's James Sanford knocked down Sudfeld's pass inside the 5-yard line.
Sudfeld was 31-of-41 for 347 yards and a touchdown for Indiana (1-1). Tevin Coleman rushed for 190 yards and three touchdowns.
The teams combined for 61 points in the second half, trading touchdowns the entire half.
In the third quarter, Knapke threw a 40-yard scoring pass to Ronnie Moore and Travis Greene scored on a 5-yard run. Indiana's Tevin Coleman scored twice in the third quarter on runs of 5 and 46 yards.
Coleman's 46-yard scoring run with 2:51 left in the third quarter gave Indiana a 28-26 lead.
Fred Coppet scored on a 1-yard run for the Falcons just 52 seconds into the fourth quarter, but the 2-point conversion pass failed and BG held a 32-28 lead.
Indiana responded with a quick four-play drive with Coleman scoring on a 31-yard run to push the Hoosiers ahead 35-32.
The Falcons then drove 88 yards for a score on a 31-yard pass from Knapke to Ryan Burbrink. With the PAT kick, Bowling Green held a 39-35 lead with 5:24 remaining in the fourth quarter.
Indiana took its final lead at 42-29 on Sudfeld's fourth-down sneak from the 1.
The Falcons responded with the eventual game-winner on Knapke's pass to Lewis. The Falcons were helped on their final drive by two pass interference penalties on Indiana, with the second penalty putting the ball at the 2.
Greene finished with 123 yards and a touchdown on 24 carries for the Falcons.
It was Bowling Green's first win over a Big Ten team since the Falcons defeated Minnesota in overtime to open the 2007 season.
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