ARLINGTON, Texas — Despite being eliminated from the playoff race when the Minnesota Vikings tripped the Houston Texans a couple hundred miles south of Cowboys Stadium, the New Orleans Saints weren’t interested in throwing in the towel Sunday.

Not by any stretch of the imagination.

Not after they watched a 14-point lead evaporate when the Dallas Cowboys, who are fighting for a playoff berth, scored two touchdowns in less than 31/2 minutes to send the game to overtime.

Not even after a near-disastrous play almost short-circuited the winning drive but instead set up Garrett Hartley’s 20-yard field goal in the Saints’ 34-31 victory.

“We just wanted to win a game and just work as hard as you can to win a game,” interim coach Joe Vitt said. “It doesn’t matter if it’s overtime or regulation, it’s to win a game. Everybody was on board. … There was no panic.”

That was evident when Tony Romo fired touchdown passes of 16 yards to Dwayne Harris and 19 yards to Miles Austin — the latter with 15 seconds remaining — to force overtime.

Then, after the Saints defense stopped the Cowboys (8-7) on four plays on their first overtime possession, the offense went the other way with the ball and quickly moved to the Cowboys’ 33, where they faced second-and-9.

Wide receiver Marques Colston caught a pass from Drew Brees on a slant pattern but had the ball stripped from his grasp at the Cowboys’ 24 by former LSU cornerback Morris Claiborne. A wild scramble ensued as tight end Jimmy Graham, who had just returned after dislocating the ring finger on his right hand while making a catch, outhustled safety Eric Frampton for the ball at the 2.

That brought in Hartley for the field goal that gave the Saints (7-8) the win and an opportunity to play for a break-even season in Sunday’s finale with the Carolina Panthers.

“I said, ‘Let’s get this kick and go home,’ ” Vitt said.

“That’s what this team does,” said Graham, who caught seven passes for 88 yards. “We have a lot of lot of resolve, and we’ve been though so much. To have that type of play and win like that here in Dallas, that’s just how this team is. We all give what we have. … That’s what is expected.”

Colston, who caught 10 passes for 153 yards, was especially thankful for Graham’s alertness. The play capped an up-and-down day for Colston, who had one drop and another fumble that went out of bounds before the Cowboys could get their hands on it.

“Yeah, that’s definitely not how you want it to end,” Colston said of his final catch, “but a great hustle play by Jimmy saved my butt.”

Colston said there was no doubt in his mind that it was a fumble even though the play was reviewed.

“I felt like it was a fumble. … I felt like I took a couple steps and just didn’t secure it tight enough,” he said. “(Claiborne) was able to get the ball and get it out pretty easily.”

It turned out to be the last pass of the day for Brees, who completed 37 of 53 passes for 446 yards — which equaled the second-highest passing total in club history — and three touchdowns in leading his team to a season-high 562 total yards.

Brees, who threw a 5-yard TD pass to Pierre Thomas to snap a 17-17 tie in the third quarter and a 3-yard scoring pass to David Thomas to extend the lead to 31-17 with 11:10 to play, said he relished the opportunity to get another shot after the Saints defense held in overtime.

“I figured that if they don’t get anything now, we just have to realize that all we need is a field goal,” Brees said. “I just wanted to get us in field-goal range, and obviously the fumble got us down to the 2. I was like, ‘Oh my gosh.’ I was so far away when he fumbled. I just ran down there.”

Brees had thrown a 6-yard touchdown to Lance Moore before the Saints got a 37-yard field goal from Hartley in the final 1:11 of the first half to take a 17-14 halftime lead. The Cowboys had wiped out a 7-0 deficit on a pair of 58-yard TD passes from Romo to Dez Bryant.

On both touchdowns, Bryant easily eluded cornerback Patrick Robinson to pull in the ball and race to the end zone.

Bryant caught nine passes for 224 yards, and Romo was 26-of-43 for 416 yards with four TDs and no interceptions to lead his team to 446 total yards.

But the Cowboys’ late scoring flurry was wasted when the Saints defense gave up an 11-yard pass from Romo to tight end Jason Witten on their first play of overtime before the next three plays netted just 5 yards and forced a punt.

“We went back out, and I told the guys, ‘We’ve got to get this,’ ” said Saints middle linebacker Curtis Lofton, who set up Pierre Thomas’ short TD run when he stripped DeMarco Murray and recovered the fumble. “ ‘We’ve got to get a three-and-out, or we’ve got to get a stop.’ ”

They did, and six plays later they were watching Graham come up with an improbable fumble recovery to bring on Hartley, who finished 2-of-3 for the day, for the chip-shot field goal.

“Offensively, we just wanted that opportunity,” Brees said. “The defense gave it to us with a big stop, then we made some big plays and had a crazy fumble recovery.

“So go figure. Everybody contributed.”