Morkel, dropped from the One-day team due to his poor batting form, inspired South Africa [ Images ] to make 62 off the last five overs and pile up an impressive total of 170 for four.
It was a good display from the Proteas who, while unfancied before the tournament, have shown they have all the elements needed for success.
A partnership of 72 between Morkel and AB de Villiers [ Images ] (47 not out) was crucial in taking the South Africans to a big total with Morkel smashing three sixes off one over from Tim Southee [ Images ].
"We played smart cricket, Albie made the most of his opportunity and his partnership with AB was probably the turning point. We controlled the game pretty well, except for some sloppiness in the final five overs. Now we have a big game against England [ Images ] coming up on Saturday," Smith said.
"Every game in this competition is crucial. We have been searching for the right combination after a little bit of a rusty start to this tournament," he added.
In response, New Zealand [ Images ] never really got into a strong rhythm and were only 39 for one after their six Power Play overs with a restricted field.
After losing opener Brendon McCullum [ Images ] in the first over to a spectacular diving catch from Gibbs off Morne Morkel [ Images ], Jesse Ryder [ Images ] (33) and Martin Guptill (18) put on a 44-run partnership at a run-rate of just 6.6 per over.
That put pressure on the middle order who failed to fire and although Nathan McCullum made a spirited 26 from 17 balls it was too late to mount a real challenge.
"You need to be inch-perfect with guys like Morkel hitting at the death, but we were a little off. We need guys at the top to play 40-50 balls to have a chance of chasing down this target," New Zealand skipper Daniel Vettori said.