Drew Brees saved the New Orleans Saints from themselves Sunday night.

Battling the aftereffects of a bruised rotator cuff, the franchise quarterback who has won so many games for the Saints was asked to win the same game twice.

Brees responded both times with the kind of throws that have made him a legend, finally burying the Dallas Cowboys 26-20 on an 80-yard touchdown pass to C.J. Spiller that pulled New Orleans back from the brink of a winless abyss.

“Right when the play call came out of Sean Payton’s mouth for C.J., I thought, ‘This is it,’ ” Brees said. “ ‘This is going the distance.’ ”

The Saints (1-3) needed Brees to pull them back from the brink of desperation.

Moments before the touchdown pass, Brees had driven the Saints down into field-goal range for a win, setting up first-year kicker Zach Hocker for a 30-yard attempt that should be automatic for most kickers.

Then, Hocker missed.

For a moment, it looked like another missed opportunity in a long line that led to three losses to open the season. The Saints defense already had failed to protect a 20-13 lead, giving up a game-tying touchdown pass to Terrance Williams on fourth down with less than two minutes left.

The drive Brees engineered should have pulled the Saints out of it.

Hocker’s miss felt like an avalanche rolling down on a team already in trouble.

“Look, you get the two-minute drive and move yourself in position and when you’re not able to hit the field goal, that can take the wind out of your sails,” Payton said. “I was proud of the guys for the win.”

New Orleans has always felt comfortable with Brees at the controls in late-game situations.

But this game was a little out of the ordinary. Brees, who had suffered a bruised rotator cuff against Tampa Bay two weeks ago, was coming off the first game he has missed due to injury in his Saints career.

For most of the night, he didn’t quite look like himself, even though he completed 33 of 41 passes for 359 yards. Whether it was any lingering pain from his shoulder injury, a Cowboys pass rush that bothered him all night or a defense that took away the deep ball, Brees spent most of the night playing within himself.

Using the same strategy that Luke McCown executed so well against Carolina, Brees piled up short completions, taking the easy throws in part because Dallas nearly picked off three throws down the field.

Brees may battle pressure throughout this season.

A depleted Dallas line working without the services of its two best pass rushers — Greg Hardy (suspension) and rookie Randy Gregory (ankle injury) — entered the game with just three sacks, and the Cowboys lost linebacker Sean Lee to a first-half concussion.

Dallas (2-2) still found a way to sack Brees three times, limiting his ability to go downfield.

Brees settled for crucial throws. Two third-down completions on the Saints’ second drive, setting up a short touchdown pass that Brees lofted over an oncoming pass rusher to Josh Hill for the 5,000th completion of his career, a number only Brett Favre and Peyton Manning had hit before.

But he saved his best for the game’s most crucial moments.

Offered a chance to win after the Cowboys tied the score at 20 with 1:51 to go, Brees opened up the downfield arm, hitting Willie Snead for 19 yards and Brandon Coleman for 30 on a beautiful back-shoulder throw that should have set up a game-winning field goal.

Instead, Brees found himself back on the field in overtime.

All he needed was an accomplice, and Brees found it in Spiller, the prized free agent signing who hadn’t found much of a role in the offense.

“You keep putting a guy in position to utilize his strengths, and eventually one hits,” Brees said. “You just kind of pick and choose your moments.”

Brees’ touchdown pass to Spiller, the fastest overtime ending in NFL history, was the 400th of his career, putting him in rarefied air with Favre, Manning, Dan Marino and Tom Brady.

And the throw drove home just how far Brees can take the Saints when the rest of the team gives him a chance. The throw to Spiller was the 34th game-winning drive of Brees’ career, a number that trails only Manning and Brady among active quarterbacks.

“Drew is our leader; having him in the huddle makes a difference,” tackle Zach Strief said. “There’s a lot to be said about believing. This kind of win can make guys believe.”