The Giants dominated most of the first half, but they managed only two field goals by Robbie Gould before Rodgers invigorated the bundled-up crowd with two touchdowns in the final three minutes. The second was spectacular, a 42-yard heave to Randall Cobb that six Giants in the end zone failed to knock down as time ran out on the half.
“As much as you want to pretend it doesn’t matter, that’s huge,” Beckham said. “That’s tough. You can kind of feel it. We didn’t come out and catch stride again. It’s unfortunate.”
Trying to finish the Giants off early in the third quarter, Green Bay Coach Mike McCarthy gambled on fourth-and-1 from Green Bay’s 43-yard line. But the Giants stuffed Ty Montgomery for a 1-yard loss, and Giants quarterback Eli Manning found Tavarres King wide open for a 41-yard touchdown to bring the Giants to within 1 point, 14-13, with 5 minutes 16 seconds left in the third quarter.
Rodgers, who finished 25 of 40 for 362 yards, struck right back with a 30-yard touchdown throw to Cobb for a 21-13 lead. The Packers added two more touchdowns and a 32-yard field goal by Mason Crosby. Cobb’s three touchdown catches tied an N.F.L. playoff record held by several players.
When it was over, Beckham cried in the locker room.
Beckham caught four passes for 28 yards in his first playoff game, and he said that the trip he and three other receivers made to Miami last Monday after a victory over the Washington Redskins had nothing to do with it.
“It put it in people’s minds that O.K., if the Giants lose, it’s because you went to Miami,” Beckham said.
He added: “At the end of the day, I went through practice, had zero drops, zero missed assignments. There was nothing that can connect seven days ago to today and how we came out and executed, nothing in the world. It’s not realistic. It created a distraction for us. It’s unfortunate, but that’s the way the world is. The connection is just not there, in my opinion, but everybody is going to have their own opinion.”
Giants Coach Ben McAdoo found no fault in his team’s effort, including Manning, who was 23 of 44 for 299 yards. But the Giants, who by the second quarter had outgained the Packers by 194 yards to 7, failed to open a large enough lead against the mercurial Rodgers, who led Green Bay to six consecutive victories to close the regular season.
Even without wide receiver Jordy Nelson, who left in the second quarter with injured ribs, Rodgers found targets all over. The Hail Mary before halftime was Rodgers’s third in 13 months.
“I think we’re starting to believe any time that ball goes up there, we’ve got a chance,” Rodgers said. “I can throw it pretty good, but it’s got to happen on the other end as well.”
None of this surprised McAdoo, Rodgers’s quarterbacks coach in Green Bay in 2012. “Any time you give Aaron those opportunities, he’s going to cash in on them, especially at home,” he said. “You’ve got to convert.”
What Rodgers showed at the end of the first half was exactly what the Giants defensive coordinator Steve Spagnuolo had warned about last week — Rodgers’s uncanny ability to improvise a perfect throw at a crucial moment.
With the ball on the Giants’ 38-yard line with 3:45 left in the first half, Rodgers slung a strike over Giants cornerback Eli Apple to wide receiver Davante Adams sprinting down the right sideline for 31 yards. Two plays later, from the 5, Rodgers shifted from side to side in the pocket to buy time, took a few steps left and threaded the ball to Adams in the end zone, with cornerback Coty Sensabaugh tight in coverage.
While the Giants failed to gain a first down on their next series, McCarthy used his final two timeouts, preserving the final 1:38. The Packers nearly ran out of time, but Jared Cook dropped a pass from Rodgers over the middle with six seconds left. A catch would have almost certainly allowed time to expire.
From the Giants’ 42, as six Giants defenders retreated to cover three Packers receivers in the end zone, Rodgers’s arcing pass fell into the hands of Cobb near the back of the end zone. Defensive backs Landon Collins, Leon Hall and Apple all jumped for the ball. Collins said he doubted that Cobb had enough room to stay in bounds, until turning around and discovering that he did.
The game carried a certain revenge factor for the Packers, who had lost to Manning and the Giants in their two previous playoff matchups, both in Green Bay. And as many have noted, the winner of a Packers-Giants postseason game has won that year’s championship in all seven previous cases. The Packers face the top-seeded Dallas Cowboys in the divisional round next Sunday at 4:40 p.m. Eastern.
The day began with gamesmanship before anyone took the field. Giants cornerback Janoris Jenkins taunted Nelson on Twitter. Jenkins wrote, “It’s Game day! Welcome back to the Rabbit Hole Jordy..#ClampSeason,” before deleting it. Jenkins is nicknamed the Jackrabbit.
It ended with Manning, who defended Beckham after the Miami trip, trying to console a tearful Beckham.
“Odell’s an emotional guy,” Manning said. “I saw him with his head down and disappointed, but there are a lot of guys who will shed a tear or two today when you lose a playoff game.
“For a lot of guys, it’s their first time in the playoffs. To kind of have the season end like that is a shock, and everybody handles it differently.”
Because of an editing error, an earlier version of this article misstated Aaron Rodgers’s playoff history against the Giants. While the Packers had lost their previous two playoff matchups against the Giants, Rodgers was the quarterback for only one of those games; he had not “lost to Manning and the Giants in their two previous playoff matchups.”