The 19-12 result meant the Fijians missed out on winning the US tournament for a third consecutive year.
Fiji hit the lead first through a typically aggressive try from Masivesi Dakuwaqa, who forced a turnover before stretching out to score.
However, a few minutes later the Blitz Bokke speedster Cecil Afrika scored under the posts which along with the easy conversion, led to a 7-5 half time score in favour of the South Africans.
The second half continued in a physical fashion with neither side prepared to give an inch at the breakdown before Afrika again showed his class to set up Chris Dry for a converted try.
Rosko Specman, who bagged the player of the final award, then looked to seal the result with a sensational 70m solo effort which left the Fiji defence grasping thin air.
However Fiji refused to lie down, scoring a Waisea Nacuqu try in dying seconds of play before a penalty from the restart ended their chances of a comeback.
South Africa have now increased their lead at the top of the series table on 107 points with Fiji second on 83, England third just two points back and New Zealand in fourth on 71.
The next tournament is in Vancouver next weekend with Fiji grouped with their Pacific rivals Samoa as well as Argentina and Wales.
Photo: World Rugby - Martin Seras Lim (The Blitz Bokke celebrate winning the Vegas Sevens)