ARLINGTON, Texas -- To Mike McCarthy, the score at halftime Sunday against the Atlanta Falcons was irrelevant. Trailing 29-10, the Dallas Cowboys' coach wanted to see how his players responded.

"This is a great opportunity to be in," McCarthy told his players. "We need this opportunity to find out about one another. Let's see what everybody has here."

As Greg Zuerlein's 46-yard field goal attempt hit the back netting with no time left to give the Cowboys the most improbable of victories, 40-39, McCarthy and the Cowboys had their answer.

"It's a new team," McCarthy said. "It's a new journey. And I tell you what, our players delivered big time."

How? By inches and some luck.

With 5 minutes, 2 seconds left, the Cowboys trailed 39-24, with the ball at the Atlanta 10.

In the past 20 seasons, teams leading by 15 or more points in the final five minutes of regulation had a record of 1,875-6 entering Sunday. The Cowboys were 25-1 underdogs to beat the Falcons at William Hill sportsbooks in Nevada in the fourth quarter.

"You're never out of the fight," Cowboys linebacker Jaylon Smith said. "This league is one where at the last minute, at the last second a lot of the times in these games that we play in, you've got to fight to the finish."

Cowboys quarterback Dak Prescott hit tight end Dalton Schultz for a touchdown, but McCarthy curiously chose to go for the 2-point conversion and the Cowboys were stopped. Instead of an eight-point hole, the Cowboys trailed 39-30. McCarthy called it "simple mathematics."

"I can't tell you how many conversations I've been involved in about this particular situation," McCarthy said. "To go for two there is just to make it clear with a little over four minutes left if we were going to be in a one-score game or a two-score game was the thinking."

As muddy as that explanation was, the defense got its first sack of Atlanta quarterback Matt Ryan when Everson Griffen dropped him for a 6-yard loss on second down and the defense forced just the second punt of the second half a play later.

Then Prescott, who became the first quarterback in NFL history to throw for 450 yards and rush for three touchdowns, went to work. He completed four of six passes for 66 yards, and that came after a 47-yard completion to Noah Brown was negated by a penalty.

Two plays later came the inches. Michael Gallup's butt cheek hit the ground before his elbow, allowing for a 38-yard gain to the Falcons' 5. During the final drive of the season-opening loss to the Rams, Gallup's deep reception was negated by offensive pass interference.

"MG just continues to show up and make huge plays time after time in one-on-one situations," Prescott said of the wide receiver. "He's a guy that I count on. He's a guy that this offense counts on in those situations. He wants his number called."

Prescott snuck in for the touchdown two plays later, but inches and luck continued to shine on the Cowboys with the ensuing onside kick.

Last season, teams converted onside kicks 10.7% of the time (six of 56) in the fourth quarter. In Week 1, one team recovered an onside kick in the fourth quarter: the Falcons.

Zuerlein's spinning kick threw the Falcons for a loop. They inexplicably let the slow roller go without jumping on it before it traveled 10 yards, giving C.J. Goodwin the chance for the recovery and the Cowboys the chance for the win.

"With the new rules, you have to have something slow where your guys can get to the ball," Zuerlein said. "In years past, you could run so you do different things. But now, you've got to have something slow. It gives our guys a chance to block and hop on it."

On second down, Prescott found rookie wide receiver CeeDee Lamb, who might have pushed an Atlanta defender, for 24 yards to put the Cowboys in position for a game-winning field goal try. Ezekiel Elliott picked up 2 yards on two runs and Prescott spiked the ball with 4 seconds to play in the game.

"I've talked about it in training camp, and I'll continue to talk about how much I believe in him," Prescott said of Lamb. "He's a player that works hard, shows up, does the right thing and wants to make those plays. He wants the ball thrown to him in those critical situations."

All that was left was for Zuerlein to make the eighth regular-season game winner of his career.

"Just swing confidently and the rest will take care of itself," Zuerlein said. "Just really be smooth. Any time I get in a hurry or don't swing confidently, bad things happen. Just swing confidently."

The second-largest comeback in Cowboys history and the second-largest of McCarthy's career was complete.

"You look at past experiences and look at any great season, you have big moments that you're able to build off of," McCarthy said. "This is a big moment to build off of, but the fact of the matter is that we're 1-1. We understand that. We want to make sure we establish home-field dominance. To come back and get that done today was outstanding. It was a great environment. The fans were a breath of fresh air to be able to be out there and compete in this great environment. It's something we can point to. We found out a lot about ourselves today."