AUSTIN -- A spot in the Sweet 16 was on the line, the University of Miami trailed by one with a minute to go, and Shane Larkin had the ball exactly where he wanted it — in his hands.

The Hurricanes’ speedy blur-of-a-guard ignored the screaming Erwin Center crowd, ignored the fact that Illinois defenders had been suffocating him all night, and launched a three-pointer to give the Hurricanes a lead they would hang onto desperately for the next 60 seconds.

Second-seeded Miami survived the seventh-seeded Illini 63-59 and are headed to the Sweet 16 for the first time since 2000 and just the second time in school history.

“It’s an amazing feeling,” Larkin said. “Growing up as a little kid, you always dream of this, and my dreams are coming true right now. ACC championship, regular-season championship. Sweet 16. I just want to keep dreaming.”

The Hurricanes are headed to Washington, where they will face No. 3 Marquette on Thursday. Marquette (25-8) struggled in its first two games, winning by a total of three points over Davidson and Butler.

“We’re just happy we’re advancing to the Sweet 16,” said UM coach Jim Larrañaga. “That’s a tremendous accomplishment. We had a very hard time scoring against their defense. Rion Brown was tremendous. We rode him for a good long while.”

Larrañaga and his staff are very familiar with the Verizon Center in Washington because it is where they led George Mason to an improbable berth to the Final Four seven years ago. It was in that building that the 11th-seeded Patriots upset top-seeded Connecticut to become only the second double-digit seed ever to reach the Final Four.

Another storybook season. And Larkin, once again, proved a hero with 17 points, including the clutch three-pointer. Brown came up huge off the bench with 21 and a pair of free throws in the final seconds.

Larkin and his teammates celebrated as the clock expired. After breathing a collective sigh of relief, they danced at midcourt as their small but spirited group of fans did the “M-I-A-M-I’’ cheer with Sebastian the Ibis. The party continued in the locker room.

“I asked you to be fighters, and you were Muhammad Ali today,’’ Larranaga told his players.

Brown made a pair of free throws with 7.7 seconds left to give UM a four-point lead and seal the win.

“I had a blast,’’ Brown said. “On the free throws, I was thinking Sweet 16, I don’t want this to end. I wanted to knock it down for the seniors.’’

Florida already had booked its ticket to the Sweet 16, and a little while later, it was the Little Team That Could — Florida Gulf Coast — shocking the nation as the first No. 15 seed ever to advance to the Round of 16.

Miami was determined to make it three-for-three from the Sunshine State. But it wouldn’t be easy.

UM players said after watching film of the Illinois team that the Illini reminded them of North Carolina, a team that likes to run and jack up threes. The game unfolded much like the ACC championship game, at a breakneck pace that had fans’ heads spinning.

The Hurricanes arrived here on Thursday determined to have fun, justify their seeding, and prove to those who still doubted that they belong in the national championship conversation. Despite an ever-growing list of milestones this season, and heaps of praise from the nation’s most respected T.V. commentators, the Hurricanes still felt a bit like outsiders among the sport’s aristocracy.