Carmen Velasquez’s voice cracked with every word, a few feet from where her son clutched a trophy and prepared to cut down the nets at Madison Square Garden. The mother of Connecticut star Shabazz Napier could barely speak, a single parent of three who screamed her way through an afternoon full of tension.

But she hadn’t been nervous. She said she never is, even when the Huskies fans around her can hardly breathe. So when Napier bounced the ball from left to right and the clock dwindled below one minute, Velasquez said she had already begun planning for next weekend. With another game on the line, she was certain what would happen next.

“We’re going to the Final Four,” said Velasquez, her premonition proved right after No. 7 seed Connecticut bested fourth-seeded Michigan State, 60-54, in Sunday’s East Region final.

A year after the Huskies were barred from participating in postseason play because of NCAA sanctions, they will face Florida, the NCAA tournament’s overall No. 1 seed, on Saturday at AT&T Stadium in Arlington, Tex., with a chance to advance to the national championship. Connecticut is the last team to beat the Gators, scoring a 65-64 victory on Dec. 2 courtesy of a Napier buzzer-beater.

It only made sense that Sunday, when the Huskies needed one more big shot, the 6-foot-1 Roxbury, Mass., native delivered again.

With Connecticut clinging to a 53-51 lead and a sellout crowd on its feet, Napier dribbled the ball from hand to hand, staring down Michigan State’s Keith Appling near the top of the key. Everybody knew who was taking the shot.

He rose and fired, and the whistle sounded. Appling had fouled him on a three-pointer, fouling out of the game. Napier then calmly stroked three free throws with 31 seconds to go for his final points of the afternoon; he finished with 25. A dunk by forward DeAndre Daniels (12 points, eight rebounds) soon followed, and the Huskies began to celebrate.

“When you have the best player on the court at the end of a game, you’re gonna win a lot of games,” former Connecticut coach Jim Calhoun said of Napier. “And he’s been the best player on the floor just about every game this year.”

Calhoun did not want to compare Napier to the school’s last NCAA tournament star, Kemba Walker, but it’s hard to ignore the parallel paths the two are taking.

In 2011, when Napier was a freshman, Walker led the Huskies on an improbable journey to a national title. Now it’s Napier’s turn to attempt the same feat.

The senior was Connecticut’s catalyst all afternoon. He added six rebounds and four assists to his scoring total and won his duel with Michigan State’s Gary Harris Jr. And he did his best work after halftime when this back-and-forth game hung in the balance.

Napier didn’t blink when Michigan State took a nine-point lead early in the second half. Instead, he glanced at Coach Kevin Ollie during a timeout and realized it was time to take over.

“When Coach looks at me a certain way, I just know I got to be more aggressive,” Napier said.

He proceeded to score six points to ignite Connecticut’s ensuing 12-0 run, hit an impossibly hard three-pointer over the outstretched arm of forward Branden Dawson and found forward Niels Giffey for a fast-break dunk.

When a fadeaway three-pointer by guard Ryan Boat­right swished through the net as the shot clock expired, Connecticut led by 10 with just more than six minutes remaining.

An electric atmosphere befitting the first region final to be played at this version of Madison Square Garden — it opened in 1968 — gave the Huskies energy from the get-go. It felt more like South Storrs, Conn.

The Spartans, meanwhile, looked like a team that had used up all its energy in a grueling Sweet 16 win over Virginia that began Friday night and ended well after midnight Saturday.

Hounded by Boatright (four steals), Michigan State committed 16 turnovers, one shy of its season high.

Despite a size advantage, Coach Tom Izzo’s team mustered just six points in the paint, and star Adreian Payne (13 points) hit only four of 14 shots.

“A couple times I came out of the huddle and I was shaking my head, like, ‘I haven’t seen this before,’ ” Izzo said.

The scene after the final buzzer was all too familiar for Connecticut. NBA alumni such as Richard Hamilton, Clifford Robinson and Andre Drummond milled around the court celebrating, a reminder of just how long the Huskies have been one of college basketball’s best.

Calhoun all but beat his chest, vindicated after passing the torch to Ollie and incredulous over how the program he built had been overlooked after conference realignment sent it to the American Athletic Conference and NCAA sanctions forced it to watch last year’s tournament from home.

And then there was Napier, walking step by step to the net as his mother wept below. For once, the moment had become too big for him.

“I was kind of flustered. I was like, ‘What’s going on?’ ” Napier said later. “It’s incredible. The way we got here, the path that we took, the work that we put in, to be stepping on that ladder and cutting down the nets, it felt special.”