GLENDALE, Ariz. — It took Mark Few 18 years as a head coach to build Gonzaga from a team no one could pronounce or find on a map to a Final Four participant. Now the Zags are a win away from something that would have been inconceivable when he arrived in Spokane as a grad assistant in 1989: a national title.

Gonzaga, the top seed in the West Regional and the No. 1 team in the country for a good chunk of the season, beat South Carolina, 77-73, on Saturday night in the first of two national semifinals at University of Phoenix Stadium.

“I don’t know that I could make a statement that would sum up, A, how I feel and B, to describe that game,” Few said after emerging from the locker room and — get this — performing a celebratory handstand. “Just ecstatic to be still playing, and to be playing the last game of the year is just crazy cool.”

The Zags (37-1), who will play North Carolina on Monday night for the title, are vying to become the first team from a non-major conference to win it since the era of such affiliations began. Gonzaga is the first from such mid-major roots to play in the final since Butler went to back-to-back title games from the Horizon League in 2010 and 2011.

That chance nearly was denied. Gonzaga’s 14-point lead early in the second half evaporated after a 16-0 run gave South Carolina a 67-65 lead with 7:06 left, but 7-footer Zach Collins’ three-pointer from the top of the arc hit the back of the rim and cascaded gently through the net to regain an advantage the Zags would never relinquish again. Collins (14 points, 13 rebounds, six blocks) had hit only 9 of 20 three-point attempts all season.

“I knew I wasn’t making plays in our last two games, so I wanted to come out and just do everything I could to give us a chance to win,” Collins said.

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Guard Nigel Williams-Goss scored 23 points for the Zags, but it was their big men who took control when it was tipping in favor of the Gamecocks (26-11). After Collins hit a three to make it 68-67, Przemek Karnowski’s two-handed dunk made it 70-67. Karnowski, the 7-1 fifth-year senior from Poland, also hit the next basket to make it 72-69.

He did all of that without being able to see clearly out of his right eye; he’d been poked there by South Carolina’s Chris Silva in the first half and there was visible redness and swelling around the socket. Karnowski was checked by an eye specialist at halftime and cleared to return.

“I had blurry vision, a little bit shadowy,” said Karnowski (13 points). “I couldn’t really open it [at first] . . . Throughout the whole second half, it was getting better and better.”

Collins hit the front end of his one-and-one with 1:35 remaining to give Gonzaga a 75-72 lead. It remained that way until 12.7 seconds remained and the ball went out of bounds off the leg of Gonzaga’s Johnathan Williams while he was chasing down an offensive rebound. That gave South Carolina a potential chance to tie the score on a three-pointer, but they never got a chance to take that shot.

Josh Perkins committed his fifth, final and most important foul of the game with 3.5 seconds left, reaching in to intentionally stop Sindarius Thornwell before he had a chance to hoist the potential tying shot. It’s a strategy some coaches shy away from. Not Gonzaga.

“We always want to foul under six [seconds],” Few said. “Perkins did a great job of being really patient and not fouling on the shot. Then the second part is you’ve got to get the rebound.”

For that, Few inserted little-used 6-10 freshman Killian Tillie. Thornwell hit the front end of his one-and-one to make it 75-73, but when he purposely missed the second shot, Tillie grabbed the rebound. He was fouled and hit two free throws with 2.2 seconds left — his 12th and 13th points of the entire tournament — to seal the win.

Thornwell, South Carolina’s senior leader, scored 15 points but shot 4-for-12 and appeared to be slowed by the remnants of the illness that caused him to miss the team’s first practice at the Final Four on Thursday. P.J. Dozier had 17 points.

South Carolina also was playing in its first Final Four and arrived as the seventh seed from the East Regional. The Gamecocks’ journey to the championship game, though, came up short. They must continue to wait for their opportunity.

For Gonzaga, that wait is over.

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“Certainly looking at what this team’s done, you can make an assumption that they’re as good as anything that’s ever walked the soil up in Spokane,” Few said. “And I wouldn’t argue with you.”