Mohammad Amir and Haris Sohail withdrew themselves from the Pakistan squad for their England tour due to personal reasons.
Pakistan reached their target off the first ball of their final over, finishing on 241/4.
According to a journalist, Haris Sohail looked exhausted during his course of play against South Africa and should have scored his century.
South Africa's fifth defeat in seven World Cup matches confirmed their embarrassingly early exit, with matches against Sri Lanka and Australia still to play.
Australia's resurgence could not have been more perfectly timed as they defend their World Cup title in England in two months.
Aaron Finch's match-winning knock overshadowed Haris Sohail's maiden one-day hundred (101 not out) which helped Pakistan to 280-5 in their 50 overs.
New Zealand, who lead the series 1-0, trail Pakistan by 394 runs with all ten wickets intact.
Azhar Ali and Haris Sohail added 126 for the third wicket as Pakistan ended Day 1 with 207 runs for the loss of four wickets.
The Aussies trail Pakistan by 452 runs with all ten wickets intact, but they face a big task ahead of them with Yasir Shah expected to wreak havoc.
Ahead of the mouth-watering clash, Pakistan batsman Haris Sohail said his team does not need any added motivation against Virat Kohli and Co.
Batsman Haris Sohail on Tuesday replaced Umar Akmal in Pakistan's ICC Champions Trophy squad after the latter failed two fitness tests during a pre-tournament camp in Birmingham.
Haris Sohail has now been taken to London for more examinations by the specialists after it was revealed that his knee operation, which he underwent in Dubai in 2015 was not successful.
Haris Sohail injured his knee during a practice session and doctors have advised him a minimum rest of two weeks.
The 26-year-old has yet to play a Test but has been a regular part of the one-day squad since 2013. He has hit seven fifties in 22 games and has a healthy average of 43.
The Pakistan batting line-up has often blown hot and cold. In this Cricket World Cup, they have shown a lot of immaturity while building an innings by throwing away good starts.
Live cricket score and ball-by-ball commentary from the 25th World Cup match between Pakistan and United Arab Emirates at the McLean Park, Napier on Wednesday.
According to media reports, Sohail woke up in the night scared, insisting there was a supernatural presence in his room. The youngster insisted on shifting to another room and by that time had developed high fever after which the team authorities pressed the hotel management to change his room immediately.
Haris Sohail scored an unbeaten 85 while Shahid Afridi made a 51-ball 61 with seven boundaries and a six as Pakistan chased down a 247-run target in 49.3 overs.