Bryant's decisive field goal came after the Falcons had blown a 27-7 fourth-quarter lead and fallen behind 28-27 after three quick Seahawks touchdowns.
Taking over with 31 seconds remaining, Matt Ryan (24-of-35, 250 yards, three TDs, two interceptions) drove the Falcons 41 yards on completions to Harry Douglas and Tony Gonzalez, and Bryant responded by driving his game-winning kick through the uprights.
Roddy White made five grabs for 76 yards and a score while Gonzalez also caught a scoring pass among his six grabs for 51 yards as top-seeded Atlanta advanced to the NFC Championship Game for the first time since 1998.
They will host the San Francisco 49ers in next week's conference title match-up.
Russell Wilson completed 24-of-36 passes for 385 yards, two scores and a pick-off while rushing seven times for 60 yards and touchdown for the Seahawks, whose furious comeback try came up short.
Zach Miller (eight catches, 142 yards) and Golden Tate (six, 103) each made a scoring grab in Seattle's loss.
2014: The Year in Music [PHOTOS]