The Saints, Super Bowl champions two years ago, raced into the post-season as the NFL's hottest team and rode that momentum to a ninth straight win to set up a divisional showdown against the San Francisco 49ers next Saturday.
"I feel like our offense, our team, is built for whatever conditions," said Brees, looking ahead to next week's game outdoors in San Francisco.
"We play indoors here but we feel we're the type of team that should be able to go anywhere, anytime and play the type of football we know how to play. We scored on every drive in the second half, I guess that's what you hope for."
Only four quarterbacks have passed for over 5,000 yards in a single NFL season and two of them, Brees and Lions' Matthew Stafford, were on the field in New Orleans promising a night of offensive fireworks at the Louisiana Superdome.
As usual, it was Brees, at the controls of the NFL's top offense, providing most of the pyrotechnics as the Saints attack piled up a post-season record of 626 total yards.
Brees, who set the new single-season passing mark, zeroed in on some play-off records completing 33 of 43 passes for 466 yards, the second most in the NFL post-season behind Bernie Kosar's 489 with the Cleveland Browns.
After a slow start, the Saints were unstoppable in the second half where Brees had all his touchdown passes, including a 56-yarder to Robert Meachem and a 41-yard strike to Devery Henderson, as New Orleans outscored Detroit 35-14 over the final two quarters.
"I thought the big plays in the second half really helped us," said Saints coach Sean Payton. "Us being able to come out to get those two (touchdowns) and we took the lead, it was really the tale of two halves.
"I think Detroit played extremely well in the first half, forced some turnover, made enough big plays offensively and really had control of the game. But we were lucky enough to get that momentum back in the third quarter."
Stafford provided his share of thrills completing 28 passes for 380 yards and three touchdowns, one to Will Heller and a pair to the NFL's leading receiver Calvin Johnson, who had 12 catches for 211 yards in his play-off debut.
Rookie JJ Watt's leaping interception return for a touchdown late in the first half put the Texans on course for victory. Third-string quarterback TJ Yates, another rookie pressed into action, then threw a 40-yard touchdown pass to Andre Johnson in the third quarter and Arian Foster followed with his second touchdown of the game, a 42-yard run in the fourth quarter, to finish off the Bengals.
After nine seasons of missing the play-offs, the Texans (11-6) are heading to play the Baltimore Ravens (12-4) next Sunday.
"This is a special day," Houston coach Gary Kubiak said.
Cincinnati were in the play-offs for the third time in seven seasons, but the Bengals (9-8) haven't advanced since beating the Houston Oilers following the 1990 season.
The Bengals outplayed the Texans for most of the first half, holding down Houston's offense and controlling time of possession, and took the lead in the first quarter on a one-yard touchdown run by Cedric Benson.
Houston drew level on the next possession, as Foster scored on an eight-yard run.
After an exchange of field goals -- Cincinnati's Mike Nugent from 37 yards and Houston's Neil Rackers from 39 -- the Texans took the lead for good late in the second quarter when Watt intercepted Cincinatti quarterback Andy Dalton and returned it 29 yards for a score, going ahead 17-10.
Watt saw this one coming, measuring his jump when Dalton dropped back and snatching the ball with both hands.
He sprinted to the end zone as the capacity crowd exploded, and he raised both hands after crossing.
Watt became the sixth defensive linemen to return an interception for a touchdown in post-season history -- excluding the Super Bowl -- and the first rookie to do it.
Dalton, meanwhile, rolled his eyes and shook his head as he walked to the Cincinnati bench and watched the replay on the giant scoreboard. It was just his second interception in his past seven games.
Late in the third quarter, Yates got away with a pass that Bengals safety Chris Crocker simply dropped. Three plays later, Johnson broke free from his cornerback and caught Yates' pinpoint pass down the sideline to put Houston up 24-10.
Foster then had a highlight reel run in the fourth quarter, dancing down the sideline for a 42-yard touchdown to complete the scoring.
Meanwhile, the New York Giants set up a mouthwatering clash against the Superbowl champions, the Green Bay Packers, next weekend as they brushed aside a shell-shocked Atlanta Falcons at Meadowlands last night.
The visitors were restricted to a first half two-point safety as Eli Manning guided his team to a 24-2 win, the franchise's first post-season win at home since 2000.