FOXBOROUGH, Mass. -- In a game in which the longest touchdown pass was thrown by receiver Julian Edelman (in his first career attempt), when the New England Patriots lined up in such a funky formation that the referee felt obligated to inform everyone in the stadium that under no circumstances should the Baltimore Ravens cover Shane Vereen since he was a "noneligible receiver," where the final play featured the oversized mitt of Rob Gronkowski trying to bat the ball away on defense, you can understand why, when the game clock finally ran out of steam, the relief among the Patriots players nearly matched the jubilance of the actual victory.

That's how it goes when you play the Ravens: a smart, physical, smashmouth team with a Joe Cool quarterback and a coaching staff that has never had any intention of kissing Bill Belichick's rings.

New England's players and staff will never admit it publicly, but we all know the truth: The Ravens were the AFC team that made them feel the queasiest, like eating bad sushi in an airport, then embarking on a turbulent flight.

Tom Brady and Julian Edelman celebrate after New England's 35-31 victory over Baltimore. AP Photo/Elise Amendola

The Patriots were right to be concerned. Baltimore held a 2-1 postseason edge over them in the Belichick/Tom Brady era and had successfully humbled New England's franchise quarterback with a four-man rush that left Brady sporting a 15.9 QBR in such situations.

When Brady threw a horrendous interception in the final minute of the first half that led to a Ravens touchdown and a 21-14 Baltimore edge at the intermission, the hushed Gillette Stadium crowd began to fret: Was it happening again?

No, it wasn't. The Ravens got to Brady in the game, too, drilling him nine times, but usually, it was after he released the ball.

Despite the pressure, when the game -- hence, the season -- was on the line, Brady delivered.

It required some innovative offensive trickery, the weekly installment of the Gronk show (seven catches, 108 yards, TD) and some late-game defensive stands, but, said receiver Brandon LaFell, it was clear to him that Brady wasn't interested in such an abrupt end to the season.

"I told him after the game [how much I appreciated him]," said LaFell, who hauled in the game's winning touchdown. "I told him, 'I've seen guys throw interceptions before the half and they just went in the tank, but you didn't do that, man. You led us, you kept preaching, you kept leading.'"

Brady threw for a postseason franchise-record 367 yards and three touchdowns in the midst of this 35-31 win, which sets an AFC championship matchup with either the Denver Broncos or Indianapolis Colts next Sunday.

He conceded it was a taxing and exhausting endeavor.

"It was -- it took a lot," Brady admitted. "It's a lot of energy, but that's what we're here for. We're supposed to go out there and make good plays."

New England made just enough of them, withstanding injuries to center Bryan Stork (knee) and cornerback Brandon Browner, who assured the assembled masses he'd be ready to go next week. For much of the season the defense has held up this team on the march toward the playoffs. On Saturday night, it was the offense that helped prop up the defense.

Brandon LaFell scores what proved to be the winning touchdown in the fourth quarter. Mark L. Baer/USA TODAY Sports

The Patriots survived letdowns that enabled Ravens running back Justin Forsett to gash them for 78 rushing yards in the first half, as well as two costly penalties delivered to Revis Island, which traditionally has been a flag-free zone. In fact, according to ESPN Stats & Information, Darrelle Revis had been hit with only three pass interference calls in his entire career before Saturday night, when he was tagged for a defensive holding call and a key interference penalty that led to a Ravens touchdown.

Defensive captain Vince Wilfork said he knows his defense can play better.

"But the most important thing right now is winning," Wilfork said. "It's not about stats -- none of that. That is so far from what these games are about. There are teams who aren't even in the playoffs that were top-ranked something."

The mantra this particular Patriots team has adopted is "Do your job." That, Wilfork said, requires mental toughness, resolve and the ability to remain calm, even when you trail by two touchdowns as late as the third quarter.

"We did all that," he said. "I'm happy. Don't care how we did it."

Ravens coach John Harbaugh doesn't feel quite the same way. When the Patriots unveiled a four offensive linemen set and identified tight end Michael Hoomanawanui as an ineligible receiver on one play, then Vereen the ineligible receiver the next, Harbaugh cried foul to no avail.

"They were worried who was eligible and who wasn't," LaFell reported. "They were fussing with each other, so we just snapped the ball quick and went on our way."

An enraged Harbaugh drew an unsportsmanlike conduct penalty which, he said afterward, was the only way he could think of to get the attention of the officials so that he could protest the lack of opportunity his team had to substitute players once the ineligible players were announced. The Patriots, Harbaugh said, tried to quick-snap the ball so the Ravens wouldn't be able to make the adjustments that should have been allotted to them.