PITTSBURGH (AP) — A most fitting comeback for Ben Roethlisberger.

With the kind of playmaking that put two Super Bowl rings on his fingers, the Steelers quarterback connected on a 58-yard pass to rookie Antonio Brown with less than two minutes to go. The go-for-broke toss set up the winning touchdown in a rough-and-tumble 31-24 victory Saturday over the archrival Baltimore Ravens.

“Let’s just chuck it deep,” Roethlisberger told offensive coordinator Bruce Arians just before he threw his biggest pass of the season. “If they pick it, it will be a pick way down there, just as good as a punt. … I just throw it as far as I can.’ “

He did.

“It was kind of amazing,” Brown said. “It kind of stuck to my shoulder.”

As a result, the Steelers (13-4) are a win away from their third Super Bowl in six seasons. The Steelers will play the winner of Sunday’s game between the New York Jets and New England Patriots.

Rashard Mendenhall scored the winning TD from 2 yards with 1:33 left. That ended any ideas the Ravens had of finally winning a playoff game against their division rivals.

Roethlisberger took his shots early from the Ravens’ defense, but threw for 226 yards and two touchdowns before his big pass on third-and-19.

“He may not be (Tom) Brady or all those other guys, but when I see him in the huddle I know we’ve got a chance to win,” said Hines Ward, who caught a TD pass. “He’s a proven winner. And history shows he’s a proven winner against Baltimore.”

The third meeting this season between these AFC North rivals had the usual skirmishes, but also was filled with penalties and turnovers.

It’s been a rugged season for the Steelers’ quarterback. His life and reputation were in tatters 10 months ago following sexual assault allegations that weren’t prosecuted. He was suspended for the first four games of the season, and helped his team finish with 12 victories and a first-round bye.

“It’s Ben. You give this guy an opportunity to snap it; he’s capable of producing plays,” Steelers coach Mike Tomlin said, “It’s not always how you draw it up, but he has a no-blink mentality. He is a competitor and a winner. And those guys follow him.”

While the Steelers trailed by two TDs at the half, it was the Ravens who fell apart in the in the second half as the team they love to beat most came back to knock them out of the postseason. The Steelers are 9-0 against division teams in the postseason.

The Steelers were trailing 21-7 after turnovers created two Ravens touchdowns. But they came back with the help of three Baltimore turnovers in the third quarter. It was so bad, the Ravens’ minus-4 yards in offense wasn’t the worst of it; they ended with 28 yards in the second half.

“We knew we had to play great. We knew if we didn’t play great we were going to lose this game,” defensive end Brett Keisel said.

Baltimore was outgained 263-126 and Joe Flacco was 16 of 30 for 125 yards.

The Ravens’ last chance to beat the Steelers — they haven’t in three postseason tries — ended when T.J. Houshmandzadeh dropped Flacco’s fourth-down pass at the Steelers’ 38 with 1:03 remaining.

“We knew it would be a close game,” Houshmandzadeh said. “I didn’t think it needed to be, but it was.”

Failing to protect the ball cost the Ravens — even after they scored two touchdowns in less than 30 seconds in the first half. Defensive end Cory Redding returned a Roethlisberger fumble for a touchdown that both teams thought was an incompletion, but that wasn’t nearly enough on a day when the Ravens’ offense did so little.

“What better way to put the Ravens out of the tournament,” Ward said. “They keep asking for us and we keep putting them out of the tournament. They’re going to be ticked about this for a long time.”

With Baltimore up 21-7, Ryan Clark forced a rare fumble by Ray Rice on a screen pass, and LaMarr Woodley recovered at the 23. The play re-energized the crowd of 64,879 that had grown silent as Baltimore opened its two-TD lead.

“You know what, our offense went in there (at halftime) and said, ‘We played terrible. We gave them the ball in prime position too many times,’ ” Roethlisberger said. “We had to do something about it.”

Mendenhall ran for 14 yards before Roethlisberger’s 9-yard scoring pass to Heath Miller, who missed two games after sustaining a concussion on a hit by Jameel McClain during the Steelers’ 13-10 win in Baltimore last month.

Later in the quarter, Flacco overthrew tight end Todd Heap, and Clark returned the interception 17 yards to the 25. Three plays later, Roethlisberger found ol’ reliable Ward, absent in the offense most of the day, for an 8-yard touchdown pass and it was tied at 21.

Along the sideline, the Ravens had the look of a team that couldn’t believe it had squandered the lead — and couldn’t figure out how to get it back. They never did.

“We felt good at the half,” Rice said. “Our defense had them stopped and I thought we were going to come out and handle our business. But then the situation happened: fumble, turnover, another turnover.”

Roethlisberger went 19 of 32 in beating the Ravens for the seventh successive time in a rivalry in which both teams had won twice by 3-point margins during the last two seasons. The asterisk: Roethlisberger didn’t play in either Steelers loss.

Baltimore turned it over for the third time in 9 minutes as center Matt Birk snapped the ball early to Flacco, who never got his hands on it, and Keisel recovered at the 23.

The drive stalled, but Shaun Suisham, who had missed earlier from the 43, converted a 35-yard field goal with 12:15 remaining to give Pittsburgh its first lead, 24-21, since its opening drive.

An apparent punt return touchdown by Lardarius Webb was negated by a holding penalty on Marcus Smith, but the Ravens — with only 36 yards of offense in the half to that point — tied it at 24 on Billy Cundiff’s 24-yard field goal with 3:54 remaining. That was too much time for Roethlisberger, who excels in fourth-quarter comebacks.

Each team took advantage of a long pass interference penalty to score during a penalty-filled first quarter. Josh Wilson’s 37-yard penalty for yanking on Mike Wallace led to Mendenhall’s 1-yard touchdown run on the Steelers’ first possession.

On a third-and-15 play, Steelers backup Anthony Madison’s 33-yard pass interference penalty set up Rice’s 14-yard TD run up the middle.

Then it really got interesting.

Terrell Suggs knocked the ball loose from the quarterback as he tried to get off a pass. Roethlisberger pump-faked, but before he could bring his right arm forward, the ball came out.

As Suggs celebrated the apparent incompletion, the ball lay on the turf for one, two, three full seconds. Haloti Ngata was closest to it but no one touched it until an alert Redding — realizing the whistle hadn’t blown — picked it up and ran it into the end zone from the 13.

Mendenhall fumbled on the Steelers’ subsequent possession, Ed Reed recovered and Flacco threw a 4-yard TD pass to Heap.

Notes: Mendenhall was the game’s leading rusher with only 46 yards on 20 carries. … Pittsburgh lost to New England 39-26 and to New York 21-16 during the season. … There were 11 sacks in the game, six by Baltimore, including three by Suggs. Pittsburgh LB James Harrison also has three sacks.