Matt Bryant kicked a 49-yard field goal with eight seconds remaining to seal the unlikely win.
The Falcons looked set to concede the biggest fourth-quarter comeback in NFL play-off history when, after leading 27-7, they fell behind to Marshawn Lynch's two-yard run with 31secs left.
But Matt Ryan completed two long passes after the kick-off to set set up Bryant's winning kick and send the Falcons to the NFC Championship game for only the third time in franchise history.
Bryant's winning moment was not without controversy, however, after he missed an initial kick only for the officials to rule a time-out had been called.
Russell Wilson passed for two touchdowns and ran for another, but it wasn't enough for the Seahawks.
The Falcons will host the San Francisco 49ers, who beat the Green Bay Packers 45-31 on Saturday, next Sunday.
Colin Kaepernick ran for a quarterback play-off record 181 yards and to leading the San Francisco 49ers back to the NFC championship game after a comfortable 45-31 victory against the Green Bay Packers.
Kaepernick, taking part in his first play-off game, outshone reigning NFL MVP Aaron Rodgers, adding two touchdown passes to wide receiver Michael Crabtree to the good work he put in with his feet.
Crabtree ended with nine receptions and 119 yards as the 49ers compiled 579 yards, with 323 of those coming on the ground.
The New England Patriots will face the Baltimore Ravens in the AFC Championship game next Sunday after Bill Belichick's side beat he Houston Texans 41-28 at Gillette Stadium.
Tom Brady registered his 17th play-off victory - the most by a quarterback - throwing three touchdowns and 344 yards.
Running back Shane Vereen scored three touchdowns two of which came from receptions as the Patriots eased to victory.
Texans quarterback Matt Schaub threw two touchdowns and 343 yards, while running back Arian Foster ran for 93 yards, but it was not enough as Brady proved too good for their defense.