Pakistan kept their World Cup hopes alive to end New Zealand's unbeaten record with a six-wicket win at Edgbaston.
New Zealand knew victory would secure a fourth successive World Cup semi-final appearance, but the Black Caps were unable to defend their total of 237 for six against revitalised opposition.
Pakistan still had plenty of work to do at the halfway mark of their chase, being 110 for three on a used pitch that was providing significant assistance to spinner Mitchell Santner.
But Babar Azam's unbeaten 101 – the first World Cup century by a Pakistan player other than an opening batsman since 1987 – saw off New Zealand with five balls to spare.
Babar passed 3,000 one-day international runs in the process, during his 68th innings and only slower than South Africa's Hashim Amla in reaching that landmark.
His 127-ball innings, which contained 11 fours, underlined the 24-year-old's huge talent, but New Zealand wicketkeeper Tom Latham was left to reflect on a spilled catch off Santner when Babar had made 38.
It was to prove a decisive drop and the result was never in doubt after that, despite Santner's spin and the early hostility generated by paceman Lockie Ferguson.
The fourth-wicket partnership between Babar and Haris Sohail, who made 68 from 66 balls before being run out in the penultimate over, was played out in front of ecstatic Pakistan supporters, who delighted in taking over Edgbaston for the day.
It was a gritty all-round team performance from Pakistan, who flew out of the blocks with Shaheen Afridi questioning New Zealand's decision to bat in overcast conditions by taking three wickets.
Their win will also raise anxiety levels in the England dressing room, with only one point now separating the two sides in the race for a top-four finish.
Furthermore, while England complete their group fixtures against India and New Zealand, two likely semi-finalists, Pakistan appear to have a kinder conclusion against Afghanistan and Bangladesh.
Mohammad Amir had first-ball success as Martin Guptill dragged on, but it was Shaheen who shone to leave New Zealand in real difficulty at 46 for four.
The out-of-form Colin Munro (12) drove to slip, Ross Taylor (three) was brilliantly caught by gloveman Sarfaraz Ahmed diving to his right, and Latham (one) also edged behind.
Afridi had figures of 7-3-11-3 from his first spell and finished with three for 28 – the most economical spell by a Pakistan bowler at the last five World Cups.
Kane Williamson, so often New Zealand's saviour, dug in, but the Black Caps skipper fell for 41 as leg-spinner Shadab Khan found prodigious turn to give Sarfaraz a third catch.
Babar Azam is a happy man right now!#CWC19 | #NZvPAK | #WeHaveWeWill pic.twitter.com/niSEOd7bnW — Cricket World Cup (@cricketworldcup) June 26, 2019
Jimmy Neesham and Colin De Grandhomme repaired the early damage with a sixth-wicket partnership of 132 as New Zealand showed their renowned battling qualities.
De Grandhomme was eventually run out for 64 and Neesham compiled an ODI best of 97 not out to set Pakistan what looked like a challenging target.
But New Zealand's wait to book that last-four spot must extend into their final two games against Australia and England.
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