New Orleans broke the postseason mark for total yards with 626, beating the record set 49 years ago.
"We were pulling out all the stops," Brees said. "We play aggressive. We're not going to apologize for that. That gives guys in the huddle a lot of confidence. We're not going to pull the reins back. It's pedal to the medal."
"This team believes," running back Arian Foster said. "I've never been around a team like this before. We don't need anyone else to believe."
In Sunday's two matchups, Atlanta (10-6) is at the New York Giants (9-7), and Pittsburgh (12-4) is at Denver (8-8).
At New Orleans, Brees was 33 of 43 while throwing for the most yards in a regulation playoff game.
Brees had plenty of help from an offense that set an NFL record for yards from scrimmage this season (7,474). The Saints (14-3) will travel to San Francisco (13-3) for next Saturday's second-round game.
All-Pro receiver Calvin Johnson had 12 receptions for 211 yards and two touchdowns in his playoff debut for Detroit, as the teams combined for 1,038 yards, tying an NFL playoff record set by Buffalo and Miami on Dec. 30, 1995.
As the game's final seconds ticked away, Houston coach Gary Kubiak walked down the sideline, a broad smile on his face, and smacked hands with players and assistant coaches.
"As soon as we settled down and got in the groove," Foster said, "we did what we do best."
Third-string quarterback T.J. Yates, a rookie pressed into action when Matt Schaub and Matt Leinart were lost for the season with injuries, threw a 40-yard touchdown pass to Andre Johnson. Foster followed with his second touchdown of the game, a 42-yard run in the fourth quarter, to finish off the Bengals (9-8).
Foster also scored on an 8-yard run in the first quarter to tie it at 7, and finished with 153 yards on 24 carries.
"The way we ran the ball today," Yates said, "it will be hard to stop us in the playoffs."
Manning, who was the Super Bowl MVP four years ago, is among a small core group remaining from the franchise's third championship team.
"We have a lot of guys on this team that haven't been in the playoffs before," Manning said. "It's a new year. We have different players. It's a new team. It's a new environment. We know what's ahead of us and we can't start looking too far up there."
The key for the Giants will be slowing Michael Turner, who rushed for 1,340 yards, and Ryan, who threw for a career-best 4,177 yards and 29 touchdowns. White is Ryan's top target, catching an NFC-leading 100 passes for 1,296 yards and eight touchdowns.
"I think we match up pretty well," White said. "They've given up 71 explosive plays, so we've got to go up there and get some. That's what we're looking to do and exploit those guys in different aspects with mismatches."
At Denver, Tim Tebow is looking to bounce back from a rough stretch with his first playoff appearance for the Broncos.
One of the NFL's most intriguing stories, Tebow won seven of his first eight starts before losing his last three while completing just 30 of 73 passes with one touchdown, four interceptions and 10 sacks to go with three lost fumbles.
"The kid does have some special qualities and he rises to the challenge on the big stage, and that's what the playoffs are all about," said former Broncos safety John Lynch, now a Fox Sports analyst. "Here's his opportunity."
Pittsburgh is considered a heavy favorite despite running back Rashard Mendenhall (knee) being out for the year and All-Pro center Maurkice Pouncey (ankle) possibly sidelined for the game. The Steelers' top tackler, safety Ryan Clark, is sitting out as a precaution because of a blood disorder that's exacerbated by altitude.
"Every year, it's something," said Doug Legursky, who would replace Pouncey - as he did in the Super Bowl last year. "As long as you stay focused on what you need to do to get the job done, that won't be a problem."