EAST RUTHERFORD, N.J. -- That top-five draft pick is slipping away with each victory. The New York Giants have now won three out of four after beating the Chicago Bears 30-27 in overtime Sunday at MetLife Stadium.

The victories serve their purpose, though. Coach Pat Shurmur and general manager Dave Gettleman are trying to build something. They've revamped the roster and tried to rebuild the culture, which has mostly been a losing one over the past few seasons. They're looking to change that and develop a winning culture within the walls at 1925 Giants Drive.

Winning on Sundays really does help. It wasn't perfect this Sunday against the Bears -- the Giants allowed a 10-point lead to slip away in the final 1 minute, 13 seconds of regulation -- but there are benefits to finishing a game, even if it took three or four tries. It's a sign that the Giants (4-8) really might be heading in the right direction internally.

"The takeaway is, and I told the team this -- I'll keep the swear words out of it -- some people are fond of talented people, some people are fond of smart people, I'm fond of tough, resilient people," Shurmur said. "When you're trying to flip culture, when you're trying to build something, you've got to really dig in on that. There was some toughness and some resiliency.

"It would have been easy to cave when they came back, an 8-3 team, came back and tied us up. They had a little bit of juice, a little bit of mojo, but our guys found a way to put points on the board and then stop them at the end. I'm fond of toughness and resiliency, and our team showed that [Sunday]."

Veteran middle linebacker Alec Ogletree is one of those players Shurmur is talking about. He was brought here in an offseason trade with that purpose. Ogletree had a pair of interceptions Sunday, including an 8-yard touchdown on the second play of the game. He also pressured Bears quarterback Chase Daniel and forced an incompletion on the final play of the contest.

Ogletree was a team captain last season for the Los Angeles Rams. He's a captain and calming presence in the locker room for the Giants. He sees what Shurmur and Gettleman are trying to accomplish.

"Yeah, I mean, just to be a professional, prepare well and do the right things," Ogletree said. "It means taking what you have learned in the classroom to the field. Like I said, things are going to be tough sometimes and you have to be able to keep fighting there and keep standing there and do your job at the highest level that you can. When you do that, it definitely changes the culture around here and it gets guys around here to play well."

It's a thin line the Giants will be walking. It’s important for them not to be fooled by this late-season surge. In 2013, the Giants won seven of their final 10 to finish 7-9 in a season that started with six consecutive losses. They brought Tom Coughlin back for another season and thought they could build off the previous one.

It proved to be fool's gold. The Giants can't believe this current team is close even if they finish strong -- which is possible with winnable games against the Redskins and Titans on deck.

Regardless, the Giants still need an influx of talent. They need a quarterback they don't have to scheme around who can be their next franchise signal-caller.

The Giants should still end with a rather high draft pick. Only four teams have fewer than four wins. The Giants are part of a muddled pack of seven teams in the four-win mix. These next four weeks (and ultimately strength of schedule as a tiebreaker) will determine where they will select in next year's draft.

The Giants' players aren't harping on that at the moment. That is the furthest thing from their minds during the season. The defense has been listening to coordinator James Bettcher preaching about his unit's need to finish off games.

It has been a struggle this season with an inconsistent pass rush and a group that has its warts in coverage. The Bears drove down the field and kicked a field goal to make it a one-score game with under two minutes remaining, then reached the end zone after recovering an onside kick.

The third time was eventually the charm for the defense. The Giants finally stopped the Bears in overtime to secure the victory. It was a sign that maybe they're learning, progressing.

"We harp on finishing the game. When we are supposed to finish the game, you just get off the field and do things the way they are supposed to be done," safety Landon Collins said. "We got a second chance and made it count."

At the very least, it's better than losing. Winning feels good on Sunday. It feels good when you wake up the following morning and throughout the week. It's a feeling the Giants are starting to experience more often.

"I think that's the whole shift they're trying to make is a winning culture, and so winning games I think is doing that," said veteran offensive lineman Nate Solder, who spent the first seven seasons of his career winning in New England. "But I think more than that is being a really solid team after a season that's been so tough, number of wins we've had and how close we've lost [games] and all those sort of things, and it speaks to the resiliency of the guys. It speaks about the type of guys we have in the locker room, and we've just got to keep going."