It is possible that no Green Bay Packers quarterback will ever make a play to match Bart Starr's sneak to win the Ice Bowl a half century ago. In subzero, subhuman conditions, Starr beat the Dallas Cowboys on sheer willpower at a time when the NFL would never consider pushing back a game like it did on Sunday for the Pittsburgh Steelers and Kansas City Chiefs.

But if the Packers win the whole thing this year like Starr's team did in 1967, they will talk about Aaron Rodgers' final pass on Sunday to beat those same Cowboys for decades to come. The great ones need memorable moments, signature plays, to frame their impact on the sport, and that 36-yard throw to Jared Cook on the sideline in the final seconds was a little like Tiger Woods' forever chip-in on Augusta National's 16th hole.

It was all about talent and touch and, more than anything, belief in the near impossible. To break the tension, Rodgers didn't enter his huddle with 35 seconds left and point to a celebrity in the stands the way Joe Montana once pointed to John Candy before leading the 49ers on a 92-yard drive to win a Super Bowl. But Rodgers did speak hopefully of his team's long-shot odds after Dallas had erased a 21-3 deficit to make it a 31-31 game, he did steady his breathing, he did declare himself "very calm" in that situation and he did express his faith in Green Bay's ability to score.

The staggering result enhanced his legacy as an all-timer, that much is clear. "At the end of the day they're going to talk about that guy as one of the top three quarterbacks who ever laced them up," said Cowboys coach Jason Garrett. "Someone said earlier this week, 'He's been hot for the last seven or eight weeks.' He's been hot since 2008."

How high can Rodgers climb the ladder now? Tom Brady has probably put this GOAT thing to bed for keeps, but Rodgers is only 33 years old and still very much at the height of his athletic powers. Maybe he can't catch Brady and his four Super Bowl titles and counting; maybe the best Rodgers can do is land in Garrett's top three, and supplant Starr and Brett Favre as the greatest Packer of them all.

He's going to need another ring, or two or three, to get there, but the final 35 seconds of this 34-31 elimination of the top-seeded Cowboys moved the needle in that direction.

Aaron Rodgers threw for 356 yards, two touchdowns and one interception in Sunday's divisional round playoff win against Dallas. Matthew Emmons/USA TODAY Sports

Start with the sack Rodgers absorbed from the blind side. How does a human manage to hold on to the football after taking that kind of hit from Jeff Heath?

Two plays later, Rodgers faced a third-and-20 from his own 32-yard line with 12 seconds to play. "I first thought he was going to try to just throw another Hail Mary," Packers president Mark Murphy said in his locker room. "I just didn't think there was any way he could get it to the end zone."

A ballet dancer in the pocket who turns into a predator on the perimeter, Rodgers took the snap and rolled to his left looking for some kind of kill shot. This time he didn't attempt another high heave. Instead, he saw Cook heading for the sideline, and he fired against the momentum of his body.

"We've made those throws before in practice," Rodgers said, "so it's a matter of trusting your muscle memory, and your training, and thinking about a positive picture when you're breaking the huddle and executing the right way."

Only this wasn't practice -- this was a divisional playoff game on the road against an opponent that was supposed to reach the Super Bowl. "Probably the best team in the NFL," Clay Matthews called the Cowboys.

On that muscle memory Rodgers talked about, his aim was pure. Cook kept his toes in play just long enough as he made the catch and fell out of bounds, and suddenly the Packers were set up for a 51-yard field goal attempt to ruin the Cowboys' charmed season.

An eight-year NFL safety and Super Bowl winner in Washington, and a longtime executive in Green Bay, Murphy said he didn't think any other current starter could've made that throw. "The combination of athleticism and strength of arm," he said, "I haven't seen it."

Murphy was asked if he knew of a retired quarterback who could've completed that pass. He paused. "You hate to bring up a Cowboy," he said, "but Roger Staubach in his prime."

Murphy agreed with a reporter's suggestion that John Elway could've also completed that pass before saying, "It's a small number."

That's why Jerry Jones, losing owner, said he has never seen an individual player do more to dictate the outcome of a game. That's why Dak Prescott, losing quarterback, said he was all but mesmerized watching his counterpart do his thing.

"It's incredible watching him," the rookie said. "I hate it in this circumstance, but he is an incredible quarterback."

After the pain subsides, Prescott will be a better quarterback for the experience. Dan Marino lost his first playoff start to Dave Krieg, who wasn't as good as Aaron Rodgers. Peyton Manning lost his first playoff start to Steve McNair, who wasn't as good as Aaron Rodgers. Elway lost his first playoff start to Mark Malone, who wasn't as good as Aaron Rodgers. They all ended up doing just fine.

Prescott was brilliant in defeat. In fact, he even posted a better quarterback rating (103.2) than Rodgers did (96.7). But Prescott was powerless to do anything about those final 35 seconds, punctuated by Mason Crosby's kick. The Cowboys' defenders were powerless, too.

"It's a great feeling to have that guy on your team," Julius Peppers said of Rodgers. "There hasn't been one time that I've been a part of this team that I went out on the field and didn't think that I had a chance to win.

"We feel like we're going to win every game with him behind center."

The Packers have done just that ever since their quarterback stared down the barrel of a four-game losing streak and 4-6 record and strongly suggested they could "run the table." They've won eight in a row, with the Falcons and the NFC Championship Game on deck.

It didn't matter that his streak of 318 consecutive passes without an interception was snapped Sunday, or that his streak of 24 touchdown passes without an interception -- the second-longest streak in NFL history to Brady's 26 in 2010, according to the Elias Sports Bureau -- also died inside AT&T Stadium. Rodgers walked out of the building with a lifetime memory nearly the equal of his one Super Bowl triumph six years ago. "This one's special," he said, "more special than we've had around here in a while."

Even without Jordy Nelson in uniform, Rodgers ran an all-day clinic of precision, athleticism and sleight-of-hand fakes. He took a few big hits, and never once blinked. Garrett helped him with an unnecessary spike of the ball on the Cowboys' final possession, ultimately giving Rodgers precious seconds to work with. But there was nobody on the Dallas side to blame for the final score. This was all about a superstar making a play that, Matthews agreed, "probably 31 other quarterbacks can't make in this league."

Rodgers quickly dismissed the idea that it was the best throw of his career, a frightening testament to his skill and competitive arrogance. But either way, Rodgers' pass in Jerry Jones' climate-controlled palace was the most dramatic play a Packer has made against the Cowboys since Starr's sneak in the Ice Bowl.

In other words, from here on out, Rodgers' primary opponent is history. He can spend the rest of this tournament and the rest of his career trying to play himself into the top five, the top three, or maybe even the top one.