Carolina has started at 3-0 for the first time in six years.
Culpepper was intercepted four times overall and almost threw as many balls to Grant as he did to star receiver Randy Moss, who was held to four catches for 16 yards.
"The three picks are lovely, but the 3-0 start, because it's a team effort, makes it wonderful," Grant said.
Culpepper committed four turnovers and Moss had just one catch in Minnesota's season-opening 24-13 loss to Carolina here in 2001. The Panthers went on to lose their next 15 games and fired George Seifert and hired John Fox as coach.
"Nothing surprises me," Fox said of Carolina's start. "Am I pleased, am I happy, am I proud of where my team is? Yes, but not surprised."
Meanwhile, new Minnesota coach Mike Tice has lost his first three games. The Vikings are 0-3 for the first time since they lost their first four games under Bud Grant in 1967.
"I felt they did a great job covering, number one," Tice said. "And number two they did a great job of keeping the quarterback off balance. I don't think Daunte ever got time to get comfortable."
Along with forcing turnovers, the Panthers had five sacks, including three by right end Mike Rucker, and shut down Minnesota's running game.
Carolina's Rodney Peete completed 20 of 30 passes for 221 yards, including a 14-yard touchdown to Steve Smith, but was intercepted twice.
"The defense kept us in the game after a couple of mistakes in the first half," Peete said. "Nobody panicked and we felt better offensively in the second half."
Peete's first interception went to cornerback Corey Chavous, who returned it 33 yards to the Carolina 17. After Moe Williams gained seven yards on third and seven, Michael Bennett scored on a one-yard run to give the Vikings a 7-0 lead 2:02 into the second quarter.
Carolina's defense set up its first score when Grant intercepted a pass by Culpepper at the Minnesota 28. Smith ran for 14 yards on the next play and Peete then hit Steve Smith with a 14-yard touchdown with 5:14 left in the third quarter.
Lamar Smith scored on runs of 12 and 24 yards in the fourth quarter to give the Panthers a 21-7 lead.
"I think we caught them off guard on the touchdowns," Smith said. "We spread them out, they were expecting the pass, the lanes opened and I just took it."
Smith's first touchdown came 1:32 into the fourth quarter and capped a six-play, 80-yard drive which featured a 32-yard pass from Peete to Steve Smith and a 20-yard pass to tight end Wesley Walls.
Panthers cornerback Reggie Howard recovered a fumble by Bennett at the Minnesota 48. After Peete hit Isaac Byrd with a 19-yard pass on third and 17, Lamar Smith scored on a 12-yard run with 7:54 left.
The Vikings responded with a nine-play, 89-yard drive which resulted in a four-yard touchdown pass by Culpepper to Chris Walsh with 3:29 remaining, pulling the Vikings within 21-14.
But on Minnesota's last possession, a long pass by Culpepper was picked off by Grant.
"We couldn't get into a rhythm," said Culpepper, who was 19 of 30 for 191 yards. "As a whole, offensively, we just haven't gotten on a roll yet. Not just Randy, myself and Michael, but everybody."
Carolina's Jon Hilbert, who was signed this week to replace the injured John Kasay, missed field-goal attempts of 45 and 39 yards.