"Unbelievable, I can't stop smiling," captain Kyle Brown said after the Boks had claimed their first victory since winning in Adelaide in 2009.

"The boys played like a family, stuck together when times were tough and, in defence, the attitude has really changed – we all worked for each other".

The Boks raced to a 19-7 half-time lead at Sam Boyd Stadium with tries from Cecil Afrika, Chris Dry and Branco du Preez, and then showed great commitment on defence to stave off a spirited comeback from Fiji after the break.

Fiji's Metieli Nacagilevu brought his team within five points of the lead, but a superb late try from Bernado Botha settled the contest.

Coach Paul Treu's team remained unbeaten throughout the pool stages of the tournament and followed through in the play-offs with a brave comeback win to beat joint series leaders England in the semi-final, after trailing 10-0 at halftime, before winning the final.

"It's awesome to know that you put in so much work in practice and then for the guys to have the ultimate belief that, when they go out on the field and stick to the things we've done, they can actually win tournaments," said a jubilant Treu.

"For the young players it's always difficult.

"They're never going to believe until they've seen it and that's what this is going to give them - that belief and calmness that when they go out there and stick to their structures that anything is possible."

Fiji earned their place in the final by thrashing New Zealand 26-7.

As a result of their win in Las Vegas, South Africa claim 24 points towards the HSBC Sevens World Series.

They remain in fifth place on 56 but close the gap on leaders England and New Zealand, who both have 80 points, as well as Samoa and Fiji, on 64 each.