FOXBOROUGH, Mass. — This is one game you don’t want to leave early.

The New England Patriots and Indianapolis Colts will meet in an AFC divisional playoff game Saturday night at Gillette Stadium. And if it follows form, the game should be decided on the final possessions.

When it comes to comebacks or winning close games, these are two of the most resilient teams in the NFL.

Down 24 points to the Denver Broncos at the half, as the Patriots were Nov. 24? No problem. New England won 34-31 in overtime.

Down 28 points to the Kansas City Chiefs just 1:21 into the third quarter, as the Colts were in their playoff game last Saturday? No problem. Indianapolis won, 45-44.

The Patriots, led by Tom Brady, won five games in the last quarter this year, none more improbable than the 27-26 win over Cleveland on Dec. 8, a game New England trailed 26-14 with 2:39 remaining. Brady has 41 career winning drives, six won in the last minute.

The Colts, led by Andrew Luck, won four games in the last quarter this year. Luck has 11 winning drives in his first two seasons, and won seven of those games after trailing by double digits.

“I think that’s what’s going to be good about this game,’’ said Devin McCourty, the Patriots’ stellar safety. “We have two teams that when you talk about mental toughness, are kind of wired the same way. We’re going to keep playing all the way to the end of the game and I think we’re going to get the same from them.’’

These teams seem to thrive on close games, so this one shouldn’t be much different. The Colts were 6-1 in games decided by one possession or less this year and are 15-2 in such games over the last two years.

The Patriots were 7-4 in one-possession games this year, the four losses by a total of 18 points, all decided on the final possession.

Beyond that they have each had to overcome significant roster losses.

The Patriots have four of their top defensive players (Vince Wilfork, Tommy Kelly, Jerod Mayo and Brandon Spikes) and two of their best offensive players (tight end Rob Gronkowski and right tackle Sebastian Vollmer) on injured reserve.

The Colts have used an NFL-high 73 players this year.

Matthew Slater, the Patriots’ talented special-teams player, said that reflects well on each organization.

“I think that obviously speaks to the leadership that’s in place,’’ said Slater. “

I think we both have good coaches. Then it says a lot about the player leadership and the mental toughness that’s there, being able to adapt through adversity and through tough situations that we’ve been in. Usually that’s the case with the teams that are left in it at this point.’’

On both teams, players stress the need to play for 60 minutes. Get a big lead, don’t let up. Get down early, don’t give up.

“Ever since I’ve been a part of this team, guys have played hard for 60 minutes,’’ said Luck, who threw four touchdown passes and scored one (on a fumbled rush) last week.

“I know in most of those games, the defense has made an unbelievable stop or forced a turnover or the special teams makes a huge play or (former Patriot Adam Vinatieri) kicks a huge field goal to win it or you get a big momentum-changing specials teams play and offensively we manage to put some decent drives together.

“I think Coach (Chuck) Pagano and the attitude he sets is to play hard for 60 minutes and overtime, if necessary, and we all buy into it.’’

Cornerback Aqib Talib said the Patriots never let the score dictate how they play, an attitude also relayed from Coach Bill Belichick.

“That’s football,’’ he said. “You’ve got to play 60 minutes and the game’s not over until 60 minutes is over.

“That’s all you hear on the sidelines when you’re down: You’ve got to play for 60 minutes. You never know what can happen so you might as well play the whole game out.’’

What happens is that one play can snowball into another and the comeback has begun.

Against the Broncos and the epic second-half comeback, a third-quarter fumble recovery by Dane Fletcher led to New England’s second touchdown. A fourth-quarter interception by Logan Ryan led to the go-ahead touchdown.

Last week, the Colts forced a key turnover and then got some luck when the ball bounced right to Luck after a fumble and he rushed in for a touchdown.

“The whole team kept fighting and that’s the key,’’ said McCourty of the Colts’ comeback. “When you see comebacks like that, it’s one play at a time. You make a play, you change the outcome of the game. You can change the momentum.’’

Belichick isn’t surprised by any of this, of course.

He says that’s just the way of the NFL. “Half the games are decided by a touchdown or less, a quarter of the games are decided by a field goal or less,’’ he said.

So what makes this season so compelling for the Patriots?

“I think our team has tried to compete hard every week,’’ he said.

“They’ve prepared well, they’ve competed hard. Some weeks it’s worked out, some weeks it hasn’t. But we’ve been in every game right to the final possession, right down to the wire.

“I’m not saying we always played right or anything but we always competed hard and put on a real high effort on the field.’’

Mike Lowe can be reached at 791-6422 or at:

mlowe@pressherald.com

Twitter: MikeLowePPH