New Zealand reached 169-2 after its target was readjusted because of a floodlight delay earlier in the game that reduced it to 19 overs per side.
Guptill shared a 76-run opening partnership with Rob Nicol (25) and a 73-run stand with captain Brendon McCullum (17), but he completely dominated both of those and New Zealand's entire innings, timing his chase just right in the thrilling last-ball win.
“I feel a whole lot better than two days ago,” Guptill said after having spent the last few days confined to his bedroom with illness.
South Africa captain Faf du Plessis and opening batsman Henry Davids earlier made half-centuries for the home team to take it to a strong total and give it a good chance to wrap up the three-game T20 series with a match to spare.
But Guptill's first century in T20 internationals ensured the Black Caps were still fighting ahead of the series decider down the coast in Port Elizabeth on Wednesday.
