Both sides lost their opening matches in the eight-nation competition in which the top two teams from each group go through to next week's semi-finals.
Pakistan, set 235 to win, lost wickets regularly and fell steadily behind the required run rate on a slow pitch, eventually succumbing for 167 all out from 45 overs.
Pakistan's 39-year-old captain Misbah-ul-Haq, who notched his highest one-day score of 96 not out in the two-wicket loss to West Indies last Friday, did his best to rally his side with 55 from 75 balls but got little support from the other batsmen.
South Africa's 234 for nine off their 50 overs was anchored by Hashim Amla, who profited from a dropped catch before he reached double figures and went on to score 81.
After AB de Villers had won the toss and elected to bat, Amla was dropped on seven when he slashed a short delivery from Mohammad Irfan to backward point.
Umar Amin, who had replaced Asad Shafiq in the Pakistan team, got the fingertips of his left hand to the ball but could not hold on to the chance.
Amla and Colin Ingram took the total to 53 in the 15th over when the latter was dismissed lbw by off-spinner Mohammad Hafeez for 20 trying to sweep.
Faf du Plessis was caught for 28 off Irfan and Amla fell at the start of the second powerplay when a reverse sweep off spinner Saeed Ajmal lobbed to Hafeez at short third man. His innings had lasted 97 balls and included nine boundaries.
The pressure on South Africa increased when Pakistan captain Misbah belied his age with consecutive runouts.
Misbah first raced to the bowler's end to whip the bails off when De Villiers slipped while trying to make his ground after he had been sent back by JP Duminy.
He then threw down the stumps at the bowler's end from short mid-wicket when it was Duminy's turn to slip after he was sent back.
Misbah was in the action again when he dived to his left in the covers to catch David Miller and there were two further runouts as the South Africans tried to accelerate.
Pakistan failed to get a good start, losing three batsmen in single figures, while opener Nasir Jamshed needed 76 deliveries to reach 42.
They took the second powerplay after 34 overs, the signal for Misbah to accelerate.
However, he ran out of partners with the potentially dangerous Kamran Akmal falling for a duck, brilliantly caught by Faf du Plessis falling to his left at backward point.
Misbah was caught by Amla at mid-wicket off Lonwabo Tsotsobe and with his departure Pakistan's faint victory hopes disappeared.
South Africa will be particularly pleased with their pace bowling in the absence through injury of their two premier fast bowlers Dale Steyn and Morne Morkel.
Morkel will play no further part in the tournament but de Villiers said Steyn would probably be fit for Friday's game against West Indies in Cardiff.
Ryan McLaren was the pick of the bowlers with four for 19 while Tsotsobe returned the miserly figures of two for 23 from nine overs. Chris Morris, making his international 50 overs debut as the replacement for Morkel, took two for 25 from seven.