The Carolina Panthers, meanwhile, find themselves in the very unexpected position of being one of two unbeaten teams left in the NFC with the almost as surprising New Orleans Saints being the other.
New England, which has not lost a game since last Nov. 18, won its 12th straight Sunday. Vinateri, who kicked the winning field goal on the last play of the Super Bowl, has provided the deciding points in 25 percent of the games during the streak.
He did it again Sunday with a 35-yarder 4:40 into overtime to give the Patriots a 41-38 win over the Kansas City Chiefs.
New England squandered a 14-point lead in the fourth quarter before pulling out the victory.
"The way I look at it, you never know what kick or what extra point is going to make the difference in the outcome of the game," Vinatieri said. "So in that sense I make sure I go out there with the same mind-set every single time, whether there is no time left or it's the first quarter."
New England is on course for a division showdown with Miami in two weeks and the Dolphins also remained unbeaten with a 30-3 decision over the New York Jets. New York had beaten Miami eight straight times before Ricky Williams helped end the jinx with a 151-yard rushing game.
"All that really matters is that it's a third win and a division win," Wannstedt said. "Jinx is something for you guys to talk about and for the fans."
A running back the Dolphins cast aside, Lamar Smith, cast aside by the Miami Dolphins, rushed for 154 yards and a pair of touchdowns for Carolina in its 21-14 win over the Minnesota Vikings.
Carolina year safety Deon Grant had three interceptions, only one fewer catches than Minnesota star receiver Randy Moss.
The Panthers are off to their first 3-0 start in six years and it comes after they lost their final 15 games last season.
"Nothing surprises me," said rookie Carolina Coach John Fox. "Am I pleased, am I happy, am I proud of where my team is? Yes, but not surprised."
Minnesota, meanwhile, is off to its first 0-3 start in 35 years.
Joining the Panthers at 3-0 is New Orleans, which finally handed the Chicago Bears a close loss, 29-23.
Chicago had won 12 straight games decided by seven points or less, but safety Sammy Knight intercepted Bears quarterback Jim Miller just shy of the end zone in the final seconds to preserve the Saints' win.
Elsewhere around the league Sunday:
-- Tim Couch rallied Cleveland in regulation and then guided the Browns into field goal range during overtime to give the Browns a 31-28 decision over Tennessee.
-- Indianapolis was able to overcome a noisy crowd in Houston to hand the expansion Texans their first home loss, 23-3.
-- Donovan McNabb accounted for 354 yards in Philadelphia's 44-13 smashing of the Dallas Cowboys.
-- Denver got an outstanding effort from quarterback Brian Griese to edge the Buffalo Bills, 28-23, and improve to 3-0.
-- San Diego stayed unbeaten and ruined Arizona's home opener with a 23-15 triumph.
-- San Francisco's defense gave Washington's wide-open offense nothing but trouble as the 49ers defeated the Redskins, 20-10.
-- In a lackluster battle of field goals, Mark Bryant kicked a career-best 47-yarder with 2;04 remaining to give the New York Giants a 9-6 win over Seattle.
-- Michael Vick threw for 174 yards and two touchdowns and ran for 54 more yards to easily carry the Atlanta Falcons to their first victory of the season, 30-3 over the Cincinnati Bengals.
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