(SportsNetwork.com) - In one of the greatest postseason games in recent memory, the New England Patriots' only lead was the final score as Tom Brady and Co. outdueled Joe Flacco and a battle-tested Baltimore Ravens team, 35-31, to reach their fourth consecutive AFC Championship Game.

In doing so the Patriots became the only team in NFL postseason history to fight back from a pair of two-touchdown deficits to win.

Brady finished 33-of-50 for 367 yards and three touchdowns, with his 50th and final toss being a go-ahead 23-yard strike to Brandon LaFell with just over five minutes remaining, a pass that was prettier than Tom Terrific's supermodel wife.

It was also Brady's 46th TD pass in the playoffs, breaking Joe Montana's all- time record.

"I don't think we played as well as we would've liked," said Brady, who completed eight of nine passes for 72 yards on the game-winning drive. "We showed a lot of toughness coming back from those two deficits."

Already the winningest postseason signal caller in NFL lore coming in, Brady was a hair better than Flacco, the most successful playoff QB since 2008 and a player that had already beaten the Pats in January at Gillette Stadium on two different occasions.

Flacco was 28-for-44 for 292 yards tossed a career postseason-best four touchdowns but his second interception of the game virtually ended Baltimore's chances with 1:39 left to play.

Flacco had thrown 197 passes and 17 TDs between postseason interceptions, the second longest streak in history, when Devin McCourty finally figured him out in the third quarter.

The University of Delaware product, who has been dubbed "January Joe" by some and "Joe Cool" by others for his unflappable demeanor in big spots, only went 11 passes before being picked again, this time by Duron Harmon in the end zone as Flacco misread a single-high safety as he went deep down the left side for Torrey Smith.

In our increasingly black-and-white society which automatically lauds winners and shuns losers with little nuance, it's Flacco's turn to take the heat for a rare mistake. But, this was like an Ali-Frazier heavyweight title fight where the only real loser was the fan who didn't see it.

The fourth postseason meeting between the Pats and Ravens in six years was an instant classic, as Flacco connected on his first eight passes, two for touchdowns to Kamar Aiken and Steve Smith, as Baltimore took an early 14-0 lead.

The Patriots got off the deck with a Brady 4-yard TD run and a 15-yard Brady to-Danny Amendola hook up late in the first half.

Brady's lone miscue -- a woefully underthrown ball that Ravens' linebacker Daryl Smith intercepted -- shifted the momentum back to the Ravens as Flacco found Owen Daniels for an 11-yard score with 10 seconds left before intermission.

Flacco's fourth TD, a 16-yarder to Justin Forsett in the third quarter, had the Charm City celebrating but New England got off the canvas again, first with a 5-yard Brady to Rob Gronkowski TD and then with a brilliant gimmick play.

With the ball at the New England 49, Brady tossed a lateral to former Kent State college QB Julian Edelman, who lofted a pass to a wide-open Amendola to deadlock the game at 28.

"We've had (the trick play) in for 10 weeks, and the coaches finally got to call it," Edelman said. "I had to loosen up the arm a little bit."

Baltimore's attempt at a third knockdown fizzled in the red zone and the Ravens settled for a Justin Tucker and a 31-28 edge.

And settling for three instead of seven was all Brady needed.

"We had two separate 14-point leads. Those guys did a good job getting it back to seven as quickly as they could," said Flacco. "They don't panic."