Atlanta will now host the San Francisco 49ers on January 20 in the National Football Conference championship game with a berth in the Super Bowl on the line.
Matt Bryant's 49-yard field goal with eight seconds to play put Atlanta ahead after the visiting Seahawks turned the game around in astonishing fashion with three touchdowns in the final quarter, almost pulling off one of the greatest National Football League play-off comebacks.
After trailing 27-7 at the end of the third, Seattle grabbed a one-point lead with 31 seconds left in the game but Bryant's kick undid all that work.
"All in all it was an extraordinary game," Seahawks coach Pete Carroll said.
The Falcons had lost their last three play-off games and the tension at the end was too much for Atlanta's veteran tight-end Tony Gonzalez in his 16th season in the league and having never won a play-off encounter.
"I was on the ground sobbing like a baby," said Gonzalez, who had insisted this would be his final attempt to reach the Super Bowl.
"I thought it was over. I've played 16 years and I thought 'here we go again,' especially with that big old lead, I guess it's just not meant to be," Gonzalez said.
It was a remarkable comeback attempt from Seattle, which would have been just the fourth time a team overcame a 20-point deficit in the post-season.
There was time for more drama as Atlanta botched the kic-koff after Bryant's field goal, allowing Seattle possession on their 46 yard line but rookie quarterback Russell Wilson's Hail Mary throw to the end zone was intercepted as time expired.
There were brows being wiped around the Georgia Dome at the end of the battle, which gave Atlanta their first play-off win in the era of head coach Mike Smith and quarterback Matt Ryan.
In the previous three attempts, Atlanta had crashed out of the play-offs without a win but for three quarters of Sunday's game they looked like a team determined to end that run.
Ryan, who threw for three touchdowns and 250 yards, found Gonzalez at the back of the end zone to make it 10-0 in the first quarter and then after another Bryant field goal, Roddy White superbly caught a 47-yard touchdown pass at full-stretch to extend the advantage to 20-0.
Wilson found Golden Tate with a 29-yard pass in the third to keep Seattle in the contest but Atlanta responded well with a superbly constructed 14-play, 80-yard drive ending in a smart five-yard Ryan pass to Jason Snelling.
At 27-7 a Falcons victory looked certain, but Wilson, who threw for 385 yards, ran in a touchdown himself and then after Ryan threw an interception, Zach Miller scored on a three-yard pass and the lead was grabbed with a two-yard run into the end-zone from Marshawn Lynch.
But Ryan was able to deliver crucial completions to Harry Douglas (22 yards) and then to trusted target Gonzalez (19 yards) to set up the game-winning kick and wild celebrations tinged with a good amount of relief.
"I have been in some wild ones but (not) at this time of year," said Ryan who finally broke his play-off duck at the fourth attempt.
"Our goal isn't to win one play-off game and to stop answering that question. Our goal is still in front of us and we have two more games to go," he said.