INDIANAPOLIS — Adam Vinatieri savored all those New England celebrations.

He made the two big field goals in the “Tuck Rule” playoff game and, of course, the two game-winning Super Bowl kicks.

On Sunday, the longtime Patriots kicker will return to his former home, possibly for the final time.

“It’s amazing,” the 42-year-old Colts kicker said when asked about his career this week. “I could never have been more lucky. If I wrote it as a book, people would never believe it.”

Believe it.

The NFL’s oldest player has played for three Super Bowl-winning coaches — Bill Parcells, Bill Belichick and Tony Dungy.

He’s played with three No. 1 draft picks — Drew Bledsoe, Peyton Manning and Andrew Luck — and a three-time Super Bowl-winning quarterback in Tom Brady. And, yes, as a rookie, Vinatieri actually did run down Dallas’ Herschel Walker on a kickoff return.

Along the way, Vinatieri filled his resume with other incredible feats.

He has four Super Bowl rings, is a perfect 6-0 on championship weekend as he makes his seventh appearance Sunday at New England (13-4).

Vinatieri also is the NFL’s career postseason scoring leader (233 points), and this weekend, he can make history in Foxborough, Massachusetts.

He will surpass Jerry Rice for most postseason games (29) in a career, if he plays Sunday, and he can break Tony Fritsch’s record for most consecutive postseason games with a field goal (13), a mark that was set during the 1970s — so long ago that even the NFL’s oldest player doesn’t remember it.

A win Sunday would send Vinatieri to another Super Bowl and give him a chance to tie Charles Haley for the most individual rings (five).

Teammates are astounded by Vinatieri’s feats.

“A lot of guys never make the playoffs,” said return specialist Josh Cribbs, a 10-year veteran who made his playoff debut Jan. 4. “For me, this is like a cherry on top of my career — just being in there.

“I’ve seen him (Vinatieri) play in a lot of games and the Super Bowl, like it’s nothing, like it’s another day. I guess a guy like that, nothing can faze him,” Cribbs added.

Perhaps nothing should faze a man who is the great, great grandson of Gen. George Custer’s bandmaster, a distant cousin of daredevil Evil Knievel and a guy who has hunted lions and bears.

Age hasn’t slowed down Vinatieri, either.

This season, he scored 140 points and became the first player in league history to top 900 points with two different franchises. Vinatieri has missed only two kicks all season — a 46-yard field goal at Tennessee in the regular-season finale and a 44-yarder at Denver last weekend.

And at the start of next year, Vinatieri will need just seven eight points to break Mike Vanderjagt’s franchise scoring record (995) and 12 points to top the 1,000-point mark with two different teams.