Babar Azam, 24, took 11 innings more than South Africa’s Hashim Amla, who reached the milestone in 57 innings, but overtook West Indies great Viv Richards (69 innings).
Hafeez was caught by Lockie Ferguson in the deep off the bowling of New Zealand captain Kane Williamson for 32 to leave Pakistan 110-3.New Zealand are second in the table on 11 points behind Australia, the only team who have qualified so far.
The top four teams qualify for the semi-finals.
Earlier, New Zealand reached 237-6 in their 50 overs, with Jimmy Neesham hitting a career-best 97 not out while Colin de Grandhomme made 64.
Left-arm seamer Shaheen Shah Afridi (3-28) starred as Pakistan reduced New Zealand to 83-5.
New Zealand were wobbling badly when the in-form Williamson was dismissed by leg-spinner Shadab Khan, who enticed the skipper into giving an edge to wicketkeeper Sarfaraz Ahmed when he was on 41.
New Zealand, who is second in the 10-team table with 11 points, kept the same team for the fifth match in a row.