ARLINGTON, Texas -- Aaron Rodgers didn't need another Hail Mary this time.

Maybe just call it a "Half Mary."

Rodgers threw a 36-yard pass to a toe-dragging Jared Cook on the sideline, and Mason Crosby kicked a 51-yard field goal on the next play as time expired, sending the Packers to the NFC championship game with their eighth straight win while thwarting a Dallas rally in a 34-31 victory in the divisional round of the playoffs Sunday.

The throw on the run from Rodgers to Cook came on third-and-20 with 12 seconds left, and after the Cowboys tied the score twice in the final 4:08 after trailing by 18 in the first half and by 15 to start the fourth quarter.

"I love the opportunity to go out there and make plays," said Rodgers, who threw for two touchdowns to give him 21 during the winning streak, although he threw his first interception during the run.

"I was disappointed we had a chance there at 28-13 to go up three scores and make it really difficult for 'em and I threw a pick there on third down. We were able to come down and have two good drives toward the end of the game."

Dallas' rally was led by rookie sensations Dak Prescott and Ezekiel Elliott in their playoff debuts, and the first two career postseason touchdown catches for star receiver Dez Bryant along with the first for 14th-year tight end Jason Witten.

"We're not going to stop no matter what the score is, no matter the game," Prescott said. "It shows the true character of this team."

Crosby's winner was the third field goal of more than 50 yards in the final 1:33 -- two from Crosby and one from Dallas' Dan Bailey. And Crosby had to make the winner twice after Dallas coach Jason Garrett called timeout before the first attempt.

"It's kind of a blur right now," Crosby said. "When we have 35 seconds on the clock and that our offense can move the ball into field goal range and a manageable kick, that's just special."

Rodgers, who sparked last week's wild-card win over the New York Giants with another Hail Mary before halftime, is headed to an MVP showdown with Atlanta's Matt Ryan next Sunday.

It will be Rodgers' third NFC title game -- all on the road for Green Bay (12-6) -- and he got there in his first game at the home of the Cowboys since he won his only title as the Super Bowl MVP six years ago.

Cook, who had six catches for a team-leading 104 yards, kept both feet inbounds with a knee just above the ground out of bounds on the decisive play. The play was confirmed on review.

"I saw him rolling to the right it was underneath coverage in front of me," Cook said. "If I got over the top of them, Aaron would put the ball in the right place. Put it right on the sideline with enough room to get my feet down. It was a heck of a throw by him."

Prescott, whose 11-game winning streak during the regular season sent Tony Romo to the bench when he returned from a preseason back injury, rallied the Cowboys in a way that probably made Dallas' 10-year starter proud.

The Cowboys (13-4) almost became the third team in the Super Bowl era to win in the playoffs after trailing by 15 in the fourth. The first was Dallas in 1972, when "Captain Comeback", Roger Staubach, rallied the Cowboys in San Francisco.

Instead, top-seeded Dallas ended up with its fifth straight loss in the divisional round and a 21-year drought in trips to the NFC championship game.

In the same position nine years ago, the Cowboys lost to the New York Giants, the biggest disappointment of Romo's tenure.

"I thought we were a team that was capable of taking this thing all the way," owner and general manager Jerry Jones said. "I know we are now after that second half."

Prescott -- a fourth-round pick who was supposed to be the No. 3 quarterback before injuries changed everything -- got Dallas' rally going with a 40-yard touchdown toss in the first half to Bryant, the first playoff TD for the star receiver.

Then he set the stage for the first tying score on a 6-yarder to Jason Witten to get within 28-20.

After a 7-yard scoring pass to Bryant -- who had nine catches for 132 yards -- Prescott ran in the tying 2-point conversion with 4:08 to go.

Rodgers led the Packers to a go-ahead 56-yard field goal from Crosby with a big boost on a pass interference penalty against rookie Anthony Brown that wiped out an interception from Jeff Heath, whose pick earlier in the game helped Dallas rally.

The Cowboys answered with a 52-yarder from Bailey with 35 seconds remaining.

ROAD WINNER

Green Bay's win was the first by a road team after 12 straight home victories in the playoffs dating to last season. The Packers were the previous road team to win -- over Washington in last season's wild-card round.

SPREADING IT AROUND

Rodgers didn't seem to miss receiver Jordy Nelson, out with a rib injury sustained in the win over the Giants. Rodgers found six different receivers, including a 34-yard touchdown to Richard Rodgers that was his longest since catching one of three successful Hail Mary passes from Aaron Rodgers in the past 13 months.

DOING THEIR PART

Prescott and Elliott missed a chance to become the first rookie QB-RB combo in the Super Bowl era to win in a playoff debut. But both did their part. Prescott threw for 302 yards and was the first rookie QB in the Super Bowl era with three TD passes in a playoff game. Elliott, the NFL rushing champion, had 125 yards.

PASSING A LEGEND

McCarthy passed Vince Lombardi and Mike Holmgren on Green Bay's coaching victory list with his 10th postseason win.

UP NEXT

Packers: At Atlanta in the NFC championship game next Sunday.

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