GLENDALE, Ariz. -- It took Gonzaga 20 NCAA Tournament appearances to make the Final Four. But one trip to the Final Four might be all the Zags need to secure a national championship.

They’re one win away now.

That’s the result of Gonzaga’s 77-73 victory over South Carolina in Saturday’s first national semifinal here at University of Phoenix Stadium. Nigel Williams-Goss led the Zags with a game-high 23 points. Zach Collins added 14 points, 13 rebounds and six blocks while South Carolina’s best player, Sindarius Thornwell, was held to just 15 points on 12 shots.

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The Zags were great offensively from the opening possession -- shooting 57.6 percent from the field, 55.6 percent from 3-point range and 100.0 percent from the free throw line in the opening 20 minutes. Six different players made at least two field goals in the first half. Williams-Goss, the reigning West Coast Conference Player of the Year, paced the effort with 12 first-half points. And Gonzaga took a 45-36 lead into the locker room despite the fact that Przemek Karnowski was sidelined for several minutes after being poked in his right eye.

Karnowski saw an eye specialist during halftime.

He was cleared to return.

So he started the second half and helped Gonzaga build a 65-51 lead with 10:55 remaining, at which point it appeared the Zags would cruise to an easy victory. But then the Gamecocks, basically out of nowhere, went on a 16-0 run to take a 67-65 lead. Wild stuff. But Collins responded with a lucky-bounce 3-pointer that gave Gonzaga a 68-67 advantage. Next possession, Karnowski got a baseline dunk for a 70-67 lead. And then Collins found Karnowski with some big-to-big action that led to an easy basket and a 72-67 advantage with 4:44 left.The Zags never trailed again.

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They’re now 37-1 on the season.

They’ll play either North Carolina or Oregon on Monday night.