Bryant's long boot followed a go-ahead scoring drive engineered by Matt Ryan, who guided the Falcons to a late victory for the third straight week.
Ryan (24-for-37, 249 yards, three interceptions) set up the decisive kick on a 13-yard completion to tight end Tony Gonzales with 12 seconds to play.
With the triumph, the Falcons moved to 6-0 for the first time in franchise history.
Oakland's Darren McFadden had tied the contest with 40 seconds left on a 2-yard scoring run.
Carson Palmer completed 23-of-33 passes for 353 yards, one TD and one interception for the Raiders (1-4).