Giants cornerback Prince Amukamara (20) celebrates with strong safety Antrel...

Giants cornerback Prince Amukamara (20) celebrates with strong safety Antrel Rolle (26) after intercepting a pass against the Houston Texans in the first quarter of a game, Sunday, Sept. 21, 2014, in East Rutherford, N.J. Credit: AP / Kathy Willens

Jason Pierre-Paul has no doubt the Giants will come away from Sunday's game against the Falcons with a victory.

"We've got to put ourselves in position to win," the defensive end said Thursday. "I think we can do it. The guys that we've got here, we're gonna do it. We're going to do it."

If they do, it would be a milestone of sorts. For the first time since the end of the 2012 season nearly 22 months ago, the Giants would be a winning team. They would be above .500.

It may not seem like an extraordinary feat, being 3-2 in a 16-game season, but consider that most of the players on the 53-man roster -- 33 of them, to be exact -- have never been here at a point when the Ws outnumbered the Ls.

"I think that's huge," cornerback Prince Amukamara said. "If we do that, it's going to be a huge message that we're sending to ourselves and sending to the league that we are for real. I think that's the type of message we need here on this team."

The Giants still are in third place behind the Eagles and Cowboys in the NFC East. They face those two teams in their next two contests after the Falcons, so if the Giants keep winning, they could be in first place by the time they reach their bye in Week 8.

But that's getting ahead of things. The first step is to tip the scales toward the wins. That makes Sunday the most significant game.

"It's huge," linebacker Jon Beason said. "You lose this game and it takes two to get ahead again. This is the most important game of your life and that's how you have to look at it."

Beason is one of those Giants who has never seen a record in the black during his time with the team. So is defensive tackle Cullen Jenkins. In fact, the last time Jenkins was on a team with a winning record was Week 4 of the 2012 season in Philadelphia. He then endured last year's 0-6 start in his first season with the Giants.

"You want to get ahead," Jenkins said. "After last year, you get tired of playing from behind. Later on in the season, it comes back to bite you. You're hoping for too many things, you're looking for help, this and that. You want to be able to control your own destiny, and it starts early in the year. Week by week, you have to get these wins."

The Giants have won two straight, as modest a streak as there can be. The key to keeping that going, Beason said, is to forget it happened.

"We were a desperate team against Houston," Beason said of the Giants' first win two weeks ago. "The house was on fire and the guys responded. You remember that feeling and try to hold on to it, keep that chip on your shoulder, and stay motivated and hungry and never be content. It feels good to win and be on a streak somewhat, but here it is, you're facing a great team . . . It doesn't get any easier."

It was defensive coordinator Perry Fewell who pointed out to his players the length of time since the Giants have sported a winning record. "You are just taking the next step," he said of what it would mean to achieve that status again. "You are showing progress from Week 3 to Week 4, Week 4 to Week 5. You are continually improving your football team. That is what we want to try to do, is continually improve and have something to show for that improvement, which is a win."

And having more of those is always a good thing.

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