Saints running back Chris Ivory rushes down the field with Lions cornerbacks Don Carey, bottom, and Amari Spievey on his heels. (AMANDA McCOY/AP)

The first NFL playoff matchup between two quarterbacks who passed for more than 5,000 yards produced an array of offensive fireworks and a much anticipated back-and-forth shootout Saturday.

But the Detroit Lions, making their first NFL playoff appearance since 1999, could not keep pace with quarterback Drew Brees and the New Orleans Saints, who displayed the prolific offense that could make them as formidable as they were during their Super Bowl-winning season two years ago.

Before a raucous crowd of 73,038 at the Superdome that included another distinguished passer, Brett Favre, Brees helped the Saints rack up 626 total yards — an all-time postseason record — and pull away for a 45-28 victory in a first-round playoff matchup.

Brees, who set an NFL record for passing yards this season, completed 33 of 43 passes for 466 yards. He had touchdown passes of 41, 3 and 56 yards.

“At times it may look easy out there,” Brees said. “But it’s not. We take great pride in going out and playing the way we did, with the exception of the turnovers. We are trying to make our mark.”

The Saints’ offense has been particularly explosive at home, where they averaged 41 points per game during the regular season. But the Saints, who are the third seed in the NFC, will now have to go on the road next weekend and play outdoors against the second-seeded San Francisco 49ers.

The Saints trailed 14-10 at halftime Saturday because of two costly fumbles in Lions’ territory. But Brees and the Saints quickly found a groove early in the third quarter. Two minutes into the quarter, Brees hooked up with wide receiver Devery Henderson for a 41-yard touchdown pass, a big-play strike that set the tenor for a second-half offensive clinic.

Saints Coach Sean Payton showed so much confidence in his offense that he went for it on fourth and one from their 38-yard line midway through the third quarter. A successful lunge by Brees kept alive a drive that culminated with tight end Jimmy Graham’s three-yard touchdown reception. Brees completed 7 of 8 passes for 94 yards during the drive that gave the Saints a 10-point lead.

“Obviously that’s a gutsy call,” Brees said of the fourth-down call with his team leading by three points. “But we have been known to make those types of calls. Maybe we didn’t even want to think about not getting it.”

The game breaker came midway through the fourth quarter, when Brees found a wide-open Robert Meachem on a deep pass for a 56-yard touchdown strike.

Some players said the Saints played the first half as if they were carrying some of the weight from last season’s disappointing first-round playoff loss at Seattle.

Saints cornerback Jabari Greer, who intercepted two passes Saturday, said: “We understood that feeling we felt on the bus, when we lost to Seattle, and then to wake up and see Matt Hasselbeck on ESPN. We can’t feel that way again. We have to focus. And guys did that. We had fun out there today.”

An overlooked facet of the Saints’ high-powered offense has been their running game, which ranked sixth in the NFL in yards per game (132.9) during the regular season. And the Saints found success on the ground throughout the game Saturday, collecting 167 rushing yards in the victory.

Darren Sproles, who has thrived while filling the role of the departed Reggie Bush this season, scored on runs of two and 17 yards.

The Saints entered the game on an eight-game winning streak, which included their 31-17 victory over Detroit in Week 13. That was a penalty-marred loss by the Lions, who also played without defensive tackle Ndamukong Suh, safety Louis Delmas and cornerback Chris Houston.

After earning the NFC’s sixth seed, the Lions entered the playoffs as healthy as they’ve been in a while, and they looked formidable right from the opening drive.

Quarterback Matthew Stafford engineered an efficient nine-play drive that covered 80 yards. The third-year quarterback completed five passes of at least 10 yards, including a 10-yard touchdown pass over the middle to tight end Will Heller.

Brees led the Saints down field just as easily. But they gave the ball back to the Lions when wide receiver Marques Colston fumbled at the Lions 18-yard line.

The Saints’ ground game proved effective early in the game. Pierre Thomas broke multiple tackles en route to a 31-yard gain. Sproles followed with a nine-yard run up the middle. That led to an effective play fake by Brees, who found wide-open fullback Jed Collins for a 15-yard pass reception.

Stafford displayed a deft touch on a number of throws during the ensuring 87-yard touchdown-scoring drive. He placed a perfectly thrown ball on the outside shoulder of wide receiver Nate Burleson. Then he floated a pass toward the back of the end zone and over two defenders for 6-foot-5 Calvin Johnson, who led the NFC with 16 receiving touchdowns, to haul in for the 16-yard reception.

Johnson finished the game with 12 receptions for 211 receiving yards.

The Lions appeared to change the complexion of the game with their defense later in the quarter. After defensive end Willie Young hit Brees’s throwing arm, linebacker Justin Durant picked up the ball at the Lions 38-yard line with nothing but open space in front of him. But an inadvertent referee’s whistle negated the potential fumble return that may have resulted in a touchdown.

In the end, the Saints and Lions combined for 1,038 total yards, which tied the most ever in a postseason game. But it was the Saints, who have one of the most explosive offenses in recent memory, who pulled away.

“Watching Drew Brees and their offense is really impressive,” Stafford said. “They put up a lot of points in the second half, and we just could not stop them.”