Buffalo Bills quarterback Josh Allen (17) reacts after an NFL football game against the New England Patriots in Foxborough, Mass., Sunday, Dec. 14. (AP photo — Charles Krupa)

ORCHARD PARK — Thrilling as the second-half comebacks have been, Josh Allen and the Buffalo Bills acknowledge that continuing to test the limits of how big of a hole they can dig themselves out of is a flawed formula for sustained success.

Each week the Bills insist they need to be better to start games. And each week — or at least the past two — they’ve somehow come away victorious.

Two weekends ago, Buffalo trailed Cincinnati by 10 points midway through the fourth quarter before scoring three touchdowns in a 4-1/2-minute span of a 39-34 win.

On Sunday, the Bills spotted New England a 21-0 second-quarter lead before Allen — in between throwing up on the sideline — oversaw five straight touchdown drives in a 35-31 win to maintain Buffalo’s slim hopes of winning a sixth straight AFC East title.

Buffalo (10-4) still trails the division-leading Patriots (11-3), who need to beat only the Jets and Miami to clinch.

“I don’t know why. It just happens,” Allen said of what’s become a game-day ritual of vomiting, after being captured on TV doing so in the fourth quarter. “It’s due to nothing else other than just a weird feeling.”

As gut-checks go, that might be an extreme one for the expectant father, after his newlywed wife, actor Hailee Steinfeld, announced her pregnancy last week.

As for the Bills’ ability to find a spark: “Obviously, we want to start faster,” Allen said. “But it’s being able to dig ourselves out and be battle-tested coming down the stretch here.”

That’s the second time in five days Allen used “battle-tested” to describe the Bills.

And, perhaps, there might be something to that in a season when Buffalo’s recent playoff rivals already have been eliminated — Kansas City and Cincinnati — while Baltimore strives to stay in contention.

AFC West-leading Denver and Houston, currently the AFC’s seventh seed, might have superior defenses. And the Bills learned how sturdy the Texans are while getting manhandled in a 23-19 loss last month.

Yet no current AFC contender can match the Bills’ postseason experience; they’ve gone 7-6 during their six-year playoff run.

Coach Sean McDermott has referred to the experience — especially the losses — as gathering scars from which the Bills can learn. It’s no different, he said Sunday, from how the team has not blinked in the face of adversity this season.

All it took on Sunday was a glimpse from Allen during halftime.

“I saw Josh as I was bringing everybody up, and he looked at me,” McDermott said. “I just knew he was seeing it like I was. The entire team was on the same vibe.”

The Bills have plenty to clean up, particularly on an injury-depleted defense that was missing top pass defender, cornerback Christian Benford, because of a toe injury.

The Bills still found a way to win, similar to how they overcame missing two starting offensive tackles in a 26-7 victory over Pittsburgh three weekends ago.

Let’s not forget how Buffalo opened the season: with Allen rallying the team from a 15-point fourth-quarter deficit against Baltimore.

The Bills are 4-1 this season when allowing 30 or more points and 7-4 when tied or trailing at halftime.

During his previous 10 seasons with the Chargers, edge rusher Joey Bosa knew mostly frustration in how his team would come up short in the clutch.

It’s different in Buffalo.

“I just don’t think there’s any quit on this team,” Bosa said. “We’ve proved that a few games this year, that you just have to keep fighting. And when you have Josh back there with the ball in his hands, anything is possible.”

What’s working

Second-half production. In winning four of five games, Buffalo has combined to outscore its opponents 111-35 over the final 30 minutes.

What needs help

First-half production. In those five games, the Bills have been outscored a combined 94-58 over the first 30 minutes.

Stock up

Ray Davis. The backup running back/kickoff returner combined for 164 yards on four returns against New England. He now leads the league averaging 32.4 yards per return.

Stock down

Defensive interior. Buffalo allowed a season-high 246 yards rushing and four touchdowns. The yards rushing were the most allowed in a Bills win since Buffalo gave up 318 in a 16-13 OT victory over the Jets in 2009.

Injuries

DT Jordan Phillips has been ruled out against Cleveland this weekend after hurting his ankle. … K Matt Prater also has been ruled out because of a quadriceps injury to his kicking leg, leading to Buffalo having to sign a replacement this week.

Key number

21 — Largest point deficit Buffalo has overcome on the road, matching a 34-31 OT win at Miami in 1987 and a 49-31 win at Cincinnati in 2010.

Next steps

Don’t peek ahead to a Week 17 showdown against Philadelphia before traveling to play Cleveland (3-11) on Sunday.