FOXBOROUGH, Mass. - If you didn't know what just had happened in one of the most exciting playoff games you'll ever see, you might have thought Bill Belichick was describing the aftermath of a loss, not an epic 35-31 win Saturday over the Ravens in an AFC divisional playoff game at Gillette Stadium.

Speaking barely above a whisper, the Patriots' coach talked about how much better his team needs to play, how much better his staff needs to coach. Uh, Bill, you just qualified for a fourth consecutive AFC Championship Game thanks to the greatest playoff comeback in franchise history. In fact, the Patriots had to overcome a 14-point deficit twice -- beating the previous 11-point comeback in the 2007 playoffs -- before advancing to the conference title game.

"Look, down 14 points twice, I don't think that's the formula to win a lot of playoff games," Belichick said. "I'm sure a lot of playoff games were lost when your team is down 14 points in the middle of the first quarter or the middle of the third quarter."

But the Patriots rallied behind another terrific performance from 37-year-old quarterback Tom Brady, who had a franchise-record 367 playoff passing yards and three touchdowns. The Patriots also relied on a trick play, with receiver Julian Edelman, a former college quarterback, throwing a perfect strike to Danny Amendola on a 51-yard touchdown in the third quarter.

Perhaps Belichick's quasi-morose tone had more to do with next week's game against the winner of Sunday's Broncos-Colts divisional matchup in Denver. "We're going to have to play a lot better, no matter who we play," he said.

But at least this was good enough against a stubborn Ravens team that had beaten the Steelers in last week's wild-card round in Pittsburgh. Joe Flacco came in with a remarkable streak of throwing a combined 13 touchdown passes and no interceptions in his last five playoff games, and he threw four touchdowns in a row against the Patriots before New England finally came up with two key interceptions in the second half, the last one sealing the game with 1:39 to play.

Brady scored the winning touchdown on a 23-yard strike to Brandon LaFell with 5:13 left in the fourth quarter. It was the Patriots' first lead . . . of the entire game.

"Tom's a great clutch player. He's tremendous," Belichick said. "He's done it with a whole lot of different receivers, a lot of different situations, so that speaks to his greatness and his ability to be consistent under pressure."

This is the ninth time Brady has gotten the Patriots to the conference championships since he became the Patriots' starter in 2001. Belichick and Brady now are a combined 8-1 in divisional-round playoff games. The only loss was to the Jets in the 2010 playoffs.

Brady showed his resilience by rallying the Patriots back to a 14-14 tie in the second quarter, and then battling back from a 28-14 second-half deficit. New England tied it 28-28 with 4:20 left in the third quarter on a trick play that hadn't run in practice since training camp.

Brady threw to his left to wide receiver Edelman, who was several yards behind the line of scrimmage. Edelman, a former college quarterback at Kent State, hit a wide-open Amendola, who was streaking down the left sideline. It was Edelman's first pass attempt in the NFL.

After Baltimore took a 31-28 lead on Justin Tucker's 25-yard field goal early in the fourth quarter, the Patriots took their only lead of the game with 5:13 to play on Brady's pinpoint touchdown throw to LaFell in the left corner of the end zone.

The touchdown was the 46th of Brady's playoff career, surpassing 49ers legend Joe Montana for the most in NFL playoff history.

"It was everything we thought it was going to be, plus more," LaFell said. "Bill [Belichick] has been preaching since last week, 'Just do your job.' That's what everybody did. Tom [Brady] had faith in me, he threw a perfect ball, and we won the game."