The Falcons (14-3) appeared ready to allow the biggest fourth-quarter comeback in NFL playoff history when Marshawn Lynch scored on a 2-yard run with 31 seconds left.
But Matt Ryan completed two long passes after the kickoff, setting up Bryant's winning kick and sending the Falcons to the NFC championship game for only the third time in franchise history. They will host the San Francisco 49ers next Sunday.
Wilson passed for two touchdowns and ran for another, but it wasn't enough for the Seahawks (12-6).
The rookie finished with 385 yards passing and did all he could to lead the Seahawks back from a 27-7 deficit entering the fourth quarter. When Lynch powered over in the final minute, a play set up by Wilson's brilliant scramble, Seattle celebrated like it would be moving on.
Not so fast.
Ryan, who had struggled in his first three playoff appearances, had just enough time to rally the Falcons. He hooked up with Harry Douglas on a 29-yard pass in front of the Falcons bench, and coach Mike Smith quickly signaled a timeout. Then, Ryan went down the middle to his favorite target, tight end Tony Gonzalez, a Hall of Famer-to-be playing what could've been his final game.
Gonzalez hauled in the 19-yard throw, and Smith called his final timeout with 13 seconds remaining.
The Seahawks called time just before the ball was snapped, and Bryant's kick sailed right of the upright. That turned out to be nothing more than practice. The next one was right down the middle, giving the Falcons a stunning victory.
Wilson's last throw, a desperation heave into the end zone, was intercepted by Falcons receiver Julio Jones.