INDIANAPOLIS (AP) — The too-perfect basketball story with the too-perfect ending is still available on DVD. The real celebration for the new national champion — that’s taking place on Tobacco Road.

Kyle Singler scored 19 points and Brian Zoubek rebounded Gordon Hayward’s miss with 3.6 seconds left Monday night to help Duke beat Butler 61-59, ending the tiny underdog’s try for a ‘‘Hoosiers’’ sequel one win short of the Hollywood ending.

The Bulldogs had a chance to win it at the end in an amazing sequence that defined this tournament. Gordon Hayward’s half-court shot at the buzzer went flying, thudded off the backboard and rim, and out and most of the crowd of 70,390 gasped, ‘‘Ohhhh.’’ So close.

The Blue Devils (35-5) snapped Butler’s 25-game winning streak and brought the long-awaited fourth national title back home to Carolina and the Cameron Crazies.

The ‘‘Big Three’’ — Singler, Jon Scheyer and Nolan Smith — won the Big One for coach Mike Krzyzewski, his first championship since 2001 and the fourth overall, tying Coach K with Adolph Rupp for second place on the all-time list.

‘‘First of all, it was a great basketball game. I want to congratulate an amazing Butler team and their fans,’’ Krzyzewski said. ‘‘Fabulous year. We played a great game, they played a great game. It’s hard for me to say it, to imagine that we’re the national champions.’’

Nobody figured this would be easy, and it wasn’t — no way that was going to happen against Butler, the 4,200-student private school that turned the tournament upside down and drove 5.6 miles from its historic home, Hinkle Fieldhouse, to the Final Four.

Butler (33-5) shaved a five-point deficit to one and had a chance to win it, when its best player, Hayward, took the ball at the top of the key, spun and worked his way to the baseline, but was forced to put up an off-balance fadeaway from 15 feet.

He missed, Zoubek got the rebound and made the first of two free throws. He missed the second one intentionally, and Duke’s title wasn’t secure until Hayward’s desperation heave bounded out.

What a game to end one of the most memorable tournaments in history, the kind that could be history if the NCAA goes ahead with what an expansion to 96 teams — something very much on the table for next year.

‘‘Both teams and all the kids on both teams played their hearts out,’’ Krzyzewski said. ‘‘There was never more than a couple, a few points separating, so a lot of kids made big plays for both teams.’’

Nobody led by more than six.

Playing against the Bulldogs and working against a crowd of 70,390 with very few pockets of Duke fans, the Blue Devils persevered — never leading by more than six but never falling behind after Singler hit a 3-pointer with 13:03 left for a 47-43 lead.

The Blue Devils won with defense. Holding the Bulldogs to 34 percent shooting and contesting every possession as tenaciously as Butler, which allowed 60 points for the first time since February. Zoubek, the 7-foot-1 center, finished with two blocks, 10 rebounds and too many altered shots to count, but also came out to trap the Butler guards and disrupt an offense that was already struggling.

They won with some clutch shooting, including Singler’s 3-for-6 effort from 3-point range and 6 of 6 from the free throw line in the second half until Zoubek’s intentional miss.

They won with a mean streak, most pointed when Lance Thomas took down Hayward hard to prevent an easy layup with 5:07 left. The refs reviewed the play and decided not to call it flagrant — one of a hundred little moments that could have swung such a tight, taut game.

In the true team fashion that has defined ‘‘The Butler Way,’’ the scoring was distributed almost perfectly even. Hayward and Shelvin Mack had 12 each. Matt Howard, coming off a concussion in the semifinal win over Michigan State, finished with 11, and 2-point-a-game scorer Avery Jukes kept Butler in it with all 10 of his points in the first half.

But Butler’s 33-year-old coach Brad Stevens was correct when he said his team couldn’t endure another 15-for-49 shooting night — what Butler shot Saturday in the semifinals. The Bulldogs went 20 for 58 this time — 34.5 percent — almost every bit as bad. All the heart in the world can’t overcome that.

‘‘I said yesterday that when you coach these guys, you can be at peace with whatever result you achieve from a won-loss standpoint because of what they gave — they gave everything we had,’’ Stevens said. ‘‘We just came up a bounce short. There’s certainly nothing to hang your head about. I told them in there, what they’ve done, what they did together, will last longer than one night, regardless of the outcome.’’