The clock was dwindling, and a charging Cowboys lineman was just feet away as Rodgers, throwing in the opposite direction of his momentum, lofted a pass roughly 40 yards in the air toward Cook.
“At that time, the quarterback’s best friend is muscle memory,” Rodgers later said. “You’re gauging your speed, the receiver’s path, the trajectory of the throw — all these things. But I’ve done it before, and you trust that memory.”
The pass settled into Cook’s hands just as he tapped both feet on the turf inside the sideline and fell out of bounds for a 36-yard gain. That perfect on-the-run throw and catch led to a 51-yard field goal by kicker Mason Crosby as time expired, the final act in Green Bay’s stirring 34-31 road victory over the Cowboys in an N.F.C. divisional-round game.
The Packers will visit the Atlanta Falcons next Sunday in the N.F.C. championship game, the team’s third appearance in a conference title game with Rodgers starting at quarterback. The Cowboys, this season’s top seed in the N.F.C., will have to wait another year to vie for a conference championship. They have not reached the title game since the 1995 season.
After Sunday’s exhilarating game — which featured multiple rallies by the Cowboys, 24 fourth-quarter points and three field goals of 50 yards or longer in the final 93 seconds — most of the talk was about Rodgers’s sparkling completion on the second-to-last play. It not only revealed his deep athletic gifts, but it also came when most teams might have been running out the clock and awaiting overtime.
“Oh, no, we had enough time,” Rodgers said of his team’s strategy. “Maybe a little too much time.”
Afterward, Rodgers was asked: Was it his best throw ever?
“No, I’ve made better ones,” Rodgers said. “And more athletic plays. It was about being patient and putting the ball in a precise place.”
But Rodgers’s teammates were in awe of the throw.
“A perfect throw, leading me across the field to where I can catch the ball and still be in bounds,” Cook said. “You almost can’t explain that talent. Except that he does it all the time.”
Or as the longtime Packers linebacker Clay Matthews said, “No game is over until Aaron’s thrown his last pass.”
For the Cowboys, that last startling completion by Rodgers helped bring a crushing end to a sterling season.
“This is a terrible feeling,” said Dak Prescott, Dallas’s rookie quarterback. “But what can I say? Aaron is an incredible quarterback. It was amazing to watch at the end, as much as I hated what was happening.”
Rodgers also went out of his way to praise Prescott, who threw for 302 yards and led the Cowboys to two fourth-quarter rallies on Sunday, and Dallas’s rookie running back, Ezekiel Elliott, who rushed for 125 yards.
“There are going to be more battles like this one over the years,” Rodgers said. “The Cowboys should be really proud of their season.”
As much as the final quarter was a seesaw affair, with two lead changes and two ties, the early part of the game was nearly a rout. In the first half, Green Bay led by 18 points and seemed to be one more score from cakewalking into the conference championship game. As late as the final quarter, the Packers led by 15 points.
But successive touchdowns in the final quarter by Dallas — and a 2-point conversion – tied the game, 28-28.
It turned out to be only the dawn of a rousing finish.
Ather the Packers took possession with about four minutes left in the fourth quarter, Rodgers quickly led them into Dallas territory. With the help of a defensive pass-interference penalty, Crosby booted a 56-yard field goal with 1 minute 33 seconds remaining.
Dallas answered with a 52-yard field goal by Dan Bailey with 58 seconds remaining.
The Packers took over at their own 25-yard line, and after four plays, they faced the third-and-20.
“We practice these kinds of plays all the time,” Rodgers said. “Down and distance and just a little bit of time.”
Crosby got his chance, and he drilled his second consecutive long field goal.
“I just kept my breathing normal, just stayed in the process like any other kick,” Crosby said. “You know it’s not just another kick, but you have to do your best to trick your brain.”
Leading by 8 points at halftime, Green Bay appeared ready to put away the Cowboys early in the third quarter, scoring quickly after intermission to go ahead, 28-13.
But Rodgers’s first interception since Nov. 13 stalled a promising drive, and the Cowboys roared back to score on Jason Witten’s 6-yard touchdown reception with 11:39 remaining in the game.
After a Packers punt, the passing of Prescott and the rushing of Elliott were instrumental on an 11-play, 80-yard drive that culminated with a 7-yard touchdown to wide receiver Dez Bryant. On a quarterback draw, Prescott then tied the game, 28-28, by running in a 2-point conversion.
“Today, two teams showed tremendous resilience, but their quarterback at the end of the day just made an outstanding, unbelievable play,” Dallas Coach Jason Garrett said. “Someday, they’ll be talking about Rodgers as one of the top three quarterbacks who ever laced them up.”
Because of an editing error, an earlier version of this article inaccurately described the decision-making of Green Bay quarterback Aaron Rodgers on the Packers’ final drive. When Rodgers took a final darting look at receiver Randall Cobb, he decided to wait for Jared Cook to keep running farther downfield and toward the sideline. Rodgers did not wait for Cobb to make that move.