Half-centuries by Marlon Samuels, Darren Sammy and Russell trumped a maiden ODI century by South Africa's David Miller as the tourists chased down a victory target of 263 with nine balls to spare.
The West Indies gained their first win in the five-match series after they several times looked doomed to defeat.
They lost their first five wickets for 73 runs against what effectively was a second string South African attack before Samuels (68) and Sammy (51) put on 93 for the sixth wicket.
Sheldon Cottrell was able to steal a single and Russell hit sixes off the next two balls from left-arm spinner Aaron Phangiso, then was able to get the strike to hit a four and a six off Kyle Abbott to finish the match.
"It means a lot," said Holder. "We have had a tough tour, so to get across the line in this match is very special."
It was a cruel result for the left-handed Miller, who made 130 not out and was responsible for a run-out and a leaping catch.
Miller came in with his side struggling at 32 for three in the seventh over. It became 76 for four when captain AB de Villiers was out for 19.
JP Duminy helped Miller add 90 for the fifth wicket but it was hard going for South Africa against a much-improved West Indian bowling performance on a slow pitch which offered some seam movement.
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