Four tries on the night - three in the second half - from the Blitzbokke helped them to victory, with tries coming from Seabelo Senatla, Steven Hunt, Philip Snyman and Cornal Hendricks.
This is now South Africa's third final win over their arch rivals this season, following earlier wins in Las Vegas and Tokyo.
VIDEO: Blitzbokke v New Zealand, highlights
Captain Frankie Horne was understandably pleased with the efforts of his team-mates.
"We put a team effort together," said Horne after the match.
"Hats off to New Zealand, they can come at you and strike at any moment.
"The guys just stuck in there and grinded and got the result."
Senatla opened the scoring for the Blitzbokke in the first minute. With nothing much on, Senatla received the ball on the left wing and with a quick turn of pace surged away from the Kiwis to score under the posts, which was converted for a 7-0 lead.
The New Zealanders, however, responded from the kickoff when Lote Raikabula ran through the SA defence at the halfway line and sprinted away to dot down. The conversion straight in front was over to square the scores at seven points apiece.
Tomasi Cama made a run for the line, and with the SA defence covering well in the seventh minute, Cama put in the perfect grubber for Kurt Baker as he crossed the whitewash to put New Zealand into the lead. Cama converted to make it 14-7 to the Kiwis.
With coach Paul Treu telling his side "no more kicking" at the interval, South Africa set about a comeback.
Senatla was involved again with eight minutes remaining in the match. After drawing two defenders his pass found Steven Hunt who had no problem gathering and crossing the line to score his side's second try. From a tight angle Philip Snyman was successful with his conversion to level the scores at 14-all.
With just over four minutes remaining, from a strong SA scrum five metres from the New Zealand line, the ball spilled loose after the Kiwis tries to kick up field out and Snyman dotted down. Snyman then added another two to take a 21-14 lead for his side.
Cornal Hendricks added the Blitzbokke's fourth try when he ran through three Kiwi defenders to stretch the lead. Snyman, again was successful with the conversion to make it 28-14.
With under a minute remaining Trinity Spooner-Neera broke through the SA defence to score under the posts which was converted to make the scores 28-21.
Despite a tense final few seconds, South Africa were able to hold on for the win.
Scorers:South Africa:
Tries: Seabelo Senatla, Steven Hunt, Philip Snyman, Cornal Hendricks
Conversions: Snyman (4)
New Zealand:
Tries: Lote Raikabula, Kurt Baker, Trinity Spooner-Neera
Conversions: Tomasi Cama (3)
Results from the Glasgow Sevens tournament on Sunday, the eighth leg of the nine-round World Sevens Series:
Bowl quarter-finals
Samoa 17 Russia 14
Australia 36 Portugal 0
France 7 Kenya 22
Scotland 31 Spain 5
Cup quarter-finals
South Africa 22 United States 5
Fiji 12 England 15
Wales 26 Canada 7
New Zealand 42 Argentina 10
Shield semi-finals
Russia 41 Portugal 7
France 41 Spain 0
Bowl semi-finals
Samoa 12 Australia 17
Kenya 24 Scotland 19
Plate semi-finals
United States 22 Fiji 7
Canada 7 Argentina 22
Cup semi-finals
South Africa 24 England 17
Wales 14 New Zealand 26
Shield final
Russia 17 France 21
Bowl final
Australia 12 Kenya 5
Plate final
United States 17 Argentina 7
Third-place match
England 24 Wales 21
Cup final
South Africa 28 New Zealand 21