The Bills then doubled their lead minutes later, this time as Fred Jackson bustled through with a four-yard run to complete the touchdown and leave his side 14-0 up.
However, in an intriguing first quarter, the Falcons were able to earn themselves seven points as Steven Jackson completed a 27-yard run to bring the score to 14-7 going into the second quarter.
Carpenter added three more points after he scored a 29-yard field goal, bringing his side's tally to 17.
The Falcons pulled themselves back within touching distance just before the end of the second as Antone Smith completed a huge 38-yard run to bring the score to 17-13.
Smith's side did not stop there, however, as Matt Bryant kicked a 49-yard field goal in the last minute to tie the contest at 17-17 going into half time.