Ben McAdoo said the biggest challenge for the Giants on Sunday was to handle their recent successes. In doing that, first they had to face the scary possibility of failure.

After falling behind by 10 points, the Giants trailed the two-win Bears by seven at halftime and seemed to be in danger of committing the inexcusable: dropping a home game to an inferior, battered opponent. All the talk about being a playoff team was on the verge of swirling down the drain. McAdoo, who had warned of the Bears’ prowess, nearly had to utter the words he never wanted to say aloud: Told ya so.

But the Giants pitched a second-half shutout against an offense that was without tight end Zach Miller and guard Josh Sitton for most of the last two quarters and had wide receiver Alshon Jeffery sidelined with a suspension. The offense, meanwhile, did just enough to pull out a 22-16 win.

On a windy day in which the teams missed three extra points and a field goal, the Giants’ postseason sails remain billowing.

The Giants (7-3) have a five-game regular-season winning streak for the first time since 2010 and are four games over .500 for the first time since 2012. They remain two games behind the Cowboys (9-1), who beat the Ravens, and ahead of Washington and Philadelphia.

“I do believe we have a championship-type atmosphere in this locker room,” Victor Cruz said. “I think we have the tools to get to [the Super Bowl]. We just have to take it one game at a time and continue to stack these Ws.”

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Dwayne Harris returned the second-half kickoff 46 yards to set up a nine-play, 56-yard drive capped by a 9-yard touchdown pass from Eli Manning to Will Tye that tied the score at 16.

After the defense forced a three-and-out, the Giants drove 79 yards in seven plays for a second straight touchdown. On third-and-4 deep in Giants territory, Manning scrambled for a first down, and on the next play, he faked as if he were going to scramble, drawing the defense forward and allowing Cruz to slip behind the secondary for a 48-yard completion. Three plays later, Manning hit rookie Sterling Shepard for a 15-yard touchdown. Robbie Gould missed his second extra point in three tries, but the Giants had a 22-16 lead.

It was the second straight game in which Shepard caught the winning touchdown.

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“He had a double move and I think killed the guy,” Manning said of Shepard’s scoring play. “I think the guy was still running the shallow route thinking that’s what he’s running. He’s done a good job just understanding the offense, understanding the timing of certain routes, how to set up things. We’ve got to keep going with that.”

In this game, they could not. The six-point lead felt precarious, especially when Harris muffed a punt (Eli Apple recovered it for the Giants) and when the Bears pinned the Giants at their 6 in the fourth quarter and when Manning nearly threw a pick-6 to Demontre Hurst with a little more than three minutes remaining. But the Giants’ defense was able to keep Chicago in check, allowing only 101 yards in the second half.

The closest the Bears came to scoring was a 51-yard field-goal attempt by Connor Barth that hit the right upright. With 1:11 left, safety Landon Collins sealed the win with his fifth interception of the season, all in the last four games.

Jason Pierre-Paul registered 1 1⁄2 of his 2 1⁄2 sacks in the fourth quarter. “I told some guys that it is time to blow up, it is on us, and guys responded,” he said of the final defensive stands. “I responded myself. I can’t just do the talking, I have to show up, and we came out with a win.”

Rashad Jennings had 85 yards and a touchdown on 21 carries, his second straight productive game. He also caught five passes for 44 yards.

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McAdoo remains wholly unimpressed by the Giants’ standing as one of the strongest playoff contenders in the NFC.

“We only played once this week,” he said. “We’re 1-0 this week. We like where we are, we liked how we finished the ballgame today with a win. We’ll get ready for next week [against the 0-11 Browns] starting [Monday].”

Yet despite the lack of any overwhelming victories — none of the Giants’ wins was by more than seven points — or big-picture enthusiasm from the coach, it’s clear that the team is beginning to forge itself as a challenger. Their seven victories already eclipse the win totals of each of the previous two seasons.

“Man,” Jennings said, “it feels good to win.”