After New Orleans' Aaron Stecker fumbled the opening kickoff, Culpepper hit Travis Taylor for a 24-yard touchdown to get the Vikings rolling.
"We had to develop some type of rhythm, some type of attitude and some type of aggression on the offensive side of the ball," Tice said. "It got us going."
Deuce McAllister's 1-yard touchdown run with under 12 minutes to go made it 24-16 before yet another mistake by New Orleans put the game out of reach.
On second-and-17 from the Saints 37, Culpepper threw a 10-yard completion to Jermaine Wiggins. But Saints defensive back Dwight Smith gave them a first down when he taunted Wiggins after tackling him.
That led to the third of four field goals by Paul Edinger, and Antoine Winfield picked off Aaron Brooks on the next possession to seal it.
The Saints, rendered nomads after Hurricane Katrina devastated their city and tore up the Superdome, were listless and sloppy again in the third consecutive road game of a season that essentially will be full of them.
They committed four turnovers and 14 penalties, one of which negated an interception in Vikings territory and another that took away a punt return for a TD by Donte Stallworth, derailing any bid for a comeback.
"We just had way too many penalties and turnovers," Saints coach Jim Haslett said. "We just didn't have any opportunities to get close to them."
Though he wouldn't admit it, Brooks looked completely drained, mentally and physically, in the locker room.
"I hope not," Brooks said, hanging his head for a long pause. "We're going to come back strong. We have to look forward to the next game. ... Hopefully we'll finally be settled into our routine there in San Antonio. That will help out a lot."
Vikings owner Zygi Wilf presented Saints owner Tom Benson with a $100,000 check for the hurricane relief effort before the game, but that was all the charity Minnesota was in the mood for after two extremely disappointing losses to start the season.
When asked if he felt sorry for the Saints' plight, cornerback Fred Smoot said, "Yeah, I do. But the dog was on our shoulders. Like I said before the game, I wish them well, but we had to give them heck."
The Vikings' defense bounced back from a horrendous showing in a 37-8 loss to Cincinnati last week, holding Joe Horn to one catch and Brooks to a 12-for-32 effort for 199 yards with one touchdown and two interceptions.
Until Culpepper, who suffered eight interceptions in the first two games, found Taylor on their first play of the game, the Vikings sorely lacked the big-play capability that defined them when Randy Moss was in purple.
That was just the beginning.
Culpepper followed an interception by Keith Newman at the Saints 26 with a 13-yard TD toss to Taylor and capped a sterling first half with a 53-yard TD to rookie Troy Williamson that made it 24-0.
"Everyone was giving those guys a hard time about the way they played for two weeks, but it's the same team without one guy," Saints safety Jay Bellamy.
"They can strike quick, and Daunte is still Daunte."
Mewelde Moore had 101 yards rushing for the Vikings, who sputtered on offense in the second half, managing only three field goals. They also allowed seven sacks.
"It's only one game," Tice said. "We've got a ways to go. We have a lot of stuff to fix."
They will play their first "home" game of the season in San Antonio next week against Buffalo, but that seemed to offer little consolation.
"Everybody can say it feels like home if they want, but they'd be lying," Bellamy said. "We just have to fight through it. It is not home and we know it's not home."
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