Imran Tahir removed Asif Ali for 11 and LBWed Andre Russell for a golden duck
, leaving Islamabad struggling at 63-5.
He got Rakep Patel caught by Paras Khadka for one and clean bowled Rushab Patel for a golden duck
Mohammad Amir removed Colin Munro for 1 and Rumman Raees dismissed captain Kane Williamson for golden duck
off a brilliant catch by Haris Sohail.
He removed Scott Borthwick for four and Ben Foakes, another Ashes squad member, for a golden duck
with successive deliveries to mean that Surrey had lost four wickets in 12 balls for just six runs.
Ball, who had already bowled opener Luke Ronchi for a golden duck
, then saw off the visiting captain's third-wicket partner Ross Taylor to begin the Kiwis' terminal slide from 158 for two to 223 all out - an outcome which ensures England will be back at the same venue for their semi-final next Wednesday.
Their bowlers, led Hasan Ali (3-24), were too hot for the Proteas' batsmen to handle, with AB de Villiers (above) collecting his first ever ODI golden duck
But after Jake Ball immediately put the chase in trouble by seeing off Luke Ronchi for a golden duck
, even the admirable Kane Williamson (87) - with his fifth successive halfcentury against England in one-day internationals - could not keep the Kiwis competitive as they were bowled out for 223 in 44.
In reply, New Zealand struggled to overcome the first over loss of Luke Ronchi for a golden duck
and, although Kane Williamson struck an assured 87, his team mates were picked off by England's impressive attack.
Zohaib went for a golden duck
and cough caught off a lose shot.
The Surrey wicketkeeper-batsman came in with the Lions on 25 for three, after a golden duck
for captain James Vince and a run out for Sam Billings.
James Anderson, who started this match seven wickets shy of Ian Botham's England record of 383 Test wickets, had opener Gautam Gambhir, trying to withdraw his bat, caught behind for a golden duck
by wicketkeeper Jos Buttler.
An angry Stokes had punched a dressing room locker at the Kensington Oval in Bridgetown for being dismissed for a golden duck
against the West Indies and had promptly broken a bone in his hand.
Stokes reacted to his dismissal for a golden duck
in Thursday's narrow victory over West Indies at the Kensington Oval by smashing the locker back in the England dressing room.
Colin Munro followed for a golden duck
moments later, caught by Elgar at short leg, and BJ Watling reached the close unbeaten on 15 - the highest score in the New Zealand side.
England fast bowler Stuart Broad struck with the first ball of the day to dismiss West Indies for 243, removing Shannon Gabriel for a golden duck
to complete test-best figures of seven for 72.