It seemed Green Bay Packers quarterback Aaron Rodgers had the New Orleans Saints defense right where he wanted them Sunday night at the Mercedes-Benz Superdome: backed up to their end zone in the third quarter with so many weapons at his disposal.

Facing a third-and-goal at the 5, Rodgers stood confidently in shotgun formation and called for the ball from rookie center Corey Linsley. Rodgers had pulled the trigger on 218 consecutive passes without throwing an interception, a string of six games dating to a season-opening loss at Seattle, tying a franchise record held by the legendary Bart Starr.

Starr still owns a share of the record, thanks to sure-handed Saints linebacker James Hawthorne, who cradled a deflected pass off the hands of Packers wide receiver Andrew Quarless at the New Orleans 2 and returned it 10 yards to the 12.

Moments later, quarterback Drew Brees and rookie wide receiver Brandin Cooks connected on a 50-yard scoring pass to give New Orleans a 23-16 lead with 5:35 remaining in the third quarter.

Green Bay never recovered, falling to 5-3 after the 44-23 loss and slipping one game behind the NFC North-leading Detroit Lions (6-2).

“That play was huge,’’ Quarless said. “We should have scored. We’re usually productive down in the red zone. I had a chance, but their defensive back made a good play.’’

“That was a big swing — a two-touchdown swing,’’ Packers coach Mike McCarthy said. “They converted it into a touchdown, so it was a big play.’’

McCarthy revealed that Rodgers injured his left hamstring on a 7-yard scramble two plays before throwing the interception.

“I conferred with our doctors on the sideline, and we decided to keep him in the game,’’ McCarthy said. “We kept him in the gun. I thought he played smart. He didn’t open himself up to further injury. He fought through the injury for a quarter and a half.’’

For the second time this season — and only the third time in NFL history — neither team punted. The teams combined for nearly 1,000 yards.

“There wasn’t a whole lot of defense played tonight, especially by us,’’ McCarthy acknowledged.

Brees threw two more touchdown passes to put the game out of reach: 22 yards to tight end Jimmy Graham in the third quarter, and 2 yards to tight end Josh Hill in the fourth quarter.

Rodgers’ next interception came just nine passes after his first one, again off the hands of a targeted Packers receiver, this time into the waiting arms of cornerback Corey White at the Saints’ 29 with 14:14 remaining.

Rodgers accounted for two touchdowns, throwing a 70-yard pass to wide receiver Randall Cobb in the first quarter, and scoring on a 14-yard scramble in the fourth quarter.

But the Saints didn’t flinch, extending their home winning streak to 20 games with coach Sean Payton on the sideline, and pushing their prime-time winning streak to 12 games.

“I don’t think they slowed us down defensively,’’ McCarthy said. “We made two penalties inside the red zone, and they got the turnovers, and that determined the game. They were the better team tonight. They ran it and they threw it better.’’