McCullum was controversially installed as skipper of all three formats recently in place of Ross Taylor, but the Black Caps sorely missed the experienced batsman in their middle order and crumpled to 86 all out after 18.2 overs.
Despite Richard Levi being dismissed for a fifth-ball duck, the Proteas were never in danger of a collapse, with captain Faf du Plessis plundering 38 not out from 32 balls and debutant wicketkeeper-batsman Quinton de Kock making an impression with an unbeaten 28.
The fall-out from Taylor being replaced as captain has still not subsided and the 28-year-old has missed the entire tour of South Africa as a result. Yet they clearly could have used his presence as the constant fall of wickets undermined their efforts to post a decent total after winning the toss.
Rob Nicol was the first to fall in the third over when he edged Rory Kleinveldt behind, while fellow opener Peter Fulton tamely hit Dale Steyn straight to mid-on.
McCullum departed next, top edging Kleinveldt to short fine-leg, and when James Franklin, Corey Anderson and Nathan McCullum fell soon after New Zealand were reeling on 36 for six. Colin Munro (23) and Doug Bracewell (21 not out) helped their side avoid total embarrassment but their efforts were inconsequential.
Kleinveldt was the pick of the bowlers with three wickets, with Steyn, Robin Peterson and Chris Morris - one of three South Africa debutants alongside De Kock and Henry Davids - picking up two scalps apiece.
The New Zealanders were always facing a losing battle with such a low total on the board although they were given some cheer when Levi edged Mitchell McClenaghan - one of four players making their first appearance for the Black Caps - to first slip.
With the total still on zero, there may have been an anxious few moments in the South African camp.
But unlike his opposite number, Du Plessis was calmness personified, striking six fours in his unbeaten knock and although South Africa lost one more wicket - Davids bowled for 20 by Ronnie Hira - their captain struck the winning runs from the first ball of the 13th over.