It’s not often that an event as old as the Final Four can produce a double first, but the 79th installment surprised us. The first of Saturday’s semifinals featured two programs making their first trip to the big stage. Neither was in a hurry to leave. Each did enough wrong to imperil its stay. In the end, a No. 1 seed held off a No. 7, if only just.

Gonzaga beat South Carolina 77-73. The clinching points were scored by Killian Tillie, a 6-foot-10 freshman from Cagnes-sur-Mer, France. He played seven minutes, leaving no impression until the final 3.5 seconds, whereupon he seized the vital rebound after the Gamecocks’ Sindarius Thornwell missed a free throw on purpose, then made two of his own.

The Bulldogs are bound for Monday’s championship game, which should surprise nobody if you believe in seeding and pedigree — Gonzaga has made every NCAA tournament since 1998 — but the Zags of the West Coast Conference have never been an easy sell. (Full disclosure: I didn’t think they’d make the Final Four.) But here they are, one game from One Shining Moment.

As happened against Northwestern in Round 2 and West Virginia in the Sweet 16, Gonzaga made this harder than it needed to be. They led 65-51 with 10:55 remaining. They trailed 67-65 with 7:06 to go. South Carolina, which had done next to nothing for most of the game, embarked on another second-half run, the likes of which had already felled Marquette, Duke and Florida. PJ Dozier, whose dad was a Gamecock, scored three baskets in the 16-0 surge, which left the precise Zags discombobulated and surely disbelieving.

Sometimes, though, a game comes down to a bounce of the ball. This one turned on a 3-point try by Gonzaga’s Zach Collins, a 7-foot freshman who’s not from France. (Las Vegas, actually.) Collins’ shot hit the brace and plopped — there’s no other word for it — through the hoop. Gonzaga was back ahead, ahead to stay. Consecutive baskets by Przemek Karnowski, a 7-1 senior from Poland, made the score 72-67. The Zags managed only three points over the final 4:41, but the Gamecocks could muster but six.

In the end, this became the defensive tug-of-war most expected. These teams ranked Nos. 1 and 2 in Ken Pomeroy’s defensive-efficiency ratings, and the final 4 1/2 minutes yielded a lot of running and bumping, but not skill. Which was OK by Gonzaga. It had the lead again. South Carolina had to catch it. South Carolina could not. The improbable run ended here.

The first half in digest form: Thornwell, who’d averaged 25.7 points in four NCAA tournament games, made one basket. (Even his make was motley — a clanged-off-the-rim 3-pointer from the left corner that bobbled home.) Thornwell worked 18 minutes, missed four shots and lost the ball twice. He managed five points, three fewer than sub Justin McKie mustered in less than half the time.

The Gamecocks hung close for a while. Gonzaga kept nosing ahead — it led for 15:58 of the 20 minutes — but South Carolina would answer with a transition basket or two, and you’d think, “This is shaping up as a real game.” Then Curtis Silva blocked Karnowski’s shot while smacking the luxuriously bearded Zag in the face. Karnowski was forced to the locker room, which might have augured a Zag sag. Nope.

The Bulldogs outscored South Carolina 14-5 over the final 5:12 — a span that included Thornwell’s lone hoop. Nigel Williams-Goss was the player of the half by some distance, and the Zags guard energized the run with a baseline fadeaway followed by a driving banker. Had the half lasted two-tenths of a second longer, his closing trey would have beaten the buzzer and put the Gamecocks a dozen points behind.

The second half began with Williams-Goss — he would finish with 23 points, five rebounds and three assists — driving the Zags into a double-figure lead, at which point it seemed class would prevailed. But South Carolina clawed its way back and gave itself a chance at the end. The chance proved unavailing. Frank Martin and his mean face and the ascendant Thornwell and his plucky crew will be seen no more this tournament, but say this for the Gamecocks: The team with the player named Notice (Duane) made us notice.

But the mystery guest from the SEC, a conference known mostly for football, will be checking out of its Phoenix hotel tomorrow. Gonzaga gets to stay through Tuesday. Gonzaga plays to win it all. Yes, Gonzaga.