FOXBOROUGH, Mass. – The New England Patriots wiped out two 14-point deficits and advanced to the AFC Championship game for the fourth straight season with a 35-31 victory over the Baltimore Ravens on Saturday.

The top-seeded Patriots, who trailed 14-0 and 28-14 in the Divisional Round playoff game, will host the winner of Sunday’s Denver-Indianapolis game at Gillette Stadium next Sunday. They are trying for their first NFL title since 2004 and their fourth overall.

Baltimore quarterback Joe Flacco threw four touchdown passes. But counterpart Tom Brady, who wasn’t very good for much of the game, was able to rally the Patriots, hitting wide receiver Brandon LaFell with a 23-yard touchdown pass with 5:13 left to give New England its only lead of the game.

The win was the first in Patriots postseason history that saw them erase a deficit of at least 12 points. They had been 0-11 previously.

The two teams combined for 850 yards of offense.

The Ravens, who barely got into the playoffs as the No. 6 seed before winning at Pittsburgh in a Wild Card game, had gone ahead when Justin Tucker kicked a 20-yard field goal with 10:17 left on a chilly night with a temperature of 20 degrees at kickoff.

New England tied the score at 28 when wide receiver Julian Edelman, a quarterback in college, took a backward pass and threw a 51-yard touchdown pass to wide receiver Danny Amendola, his second touchdown catch of the game. It was Edelman’s first pass as a pro.

Baltimore, 2-1 in its last three postseason games at New England, moved the ball from its 11 to the New England 36, but safety Duron Harmon picked Flacco off in the end zone with 1:39 left. It was the second interception of Flacco, who earlier ran a streak of passes without an interception to 197, the second longest in postseason history.

New England then had to punt the ball with 14 seconds left, but the Ravens did nothing with it.

The win was the 20th in the postseason for Patriots coach Bill Belichick, moving him into a tie with Tom Landry for the all-time lead.

Brady threw three touchdown passes, giving him 46 for his career in the postseason, an NFL record. He passed for 367 yards, a franchise record, and also ran for a touchdown in a game that saw the Patriots rush for just 14 yards.

Brady was 33 of 50 with an interception. The 33 completions were a club record. He also moved into the all-time lead in passing yards, but Denver’s Peyton Manning will take that back on Sunday. It was Brady’s seventh career postseason 300-yard passing game, second all time, and his NFL-record 19th career postseason win.

Flacco was 28 of 44 for 292 yards.

Ravens running back Justin Forsett ran for 129 yards on 24 carries in the loss.

Patriots tight end Rob Gronkowski caught seven passes for 108 yards, his second career postseason 100-yard game.

Long marches the first two times they had the ball gave the Ravens their 14-0 lead with 4:44 left in the first quarter, but the score was tied 3:37 into the second quarter.

Baltimore scored the next 14 points. One touchdown came before the end of the first half after Brady was picked off by linebacker Daryl Smith and the other on its first drive of the second half.

Back came the Patriots again, tying it on the flea-flicker, and they appeared set to take the lead after a sack by linebacker Jamie Collins shook the ball loose from Flacco. Collins recovered the ball, but Patriots cornerback Darrelle Revis, who had a tough game, was called for holding.

The drive alive, Flacco continued a drive that lasted almost eight minutes and ended with Tucker’s field goal.

Patriots running back Shane Vereen then fumbled the ball away at midfield, but the call was overturned because he was down by contact.

NOTES: Patriots QB Tom Brady tied Curtis Martin’s franchise record with his fifth postseason rushing touchdown. … NFL commissioner Roger Goodell sat out in the cold for the game. He wore a baseball cap with a ‘B’ on it. Boston? Baltimore? … With his 15th playoff start, Ravens QB Joe Flacco set an NFL record for postseason starts by a quarterback in his first seven years. … Patriots C Brian Stork left the game in the second quarter with a knee injury and RG Ryan Wendell moved over. … Patriots coach Bill Belichick had been tied with Don Shula for second place on the career postseason wins list before the win moved him into a tie with Tom Landry for No. 1. … The Ravens set a franchise record with 409 points in the regular season before scoring 30 in their wild Card win over the Pittsburgh Steelers. … Rookie RB Jonas Gray, who missed New England’s final regular-season game with an ankle injury, was among the inactives.