New Zealand, set a daunting 280-run target against a potent Pakistan bowling attack were 35 for one in 6.5 overs when rain halted play.
Pakistan gave themselves a bright chance of sealing a series win after Babar Azam's 92 guided them to a challenging 279/8 in Dubai.
The first of three Tests with New Zealand starts on November 16 in Abu Dhabi, with the same venue also staging the series finale from December 3.
In crunch games, historically sides batting first, are generally more likely to win and the Pakistan captain was right in his wisdom for bowling second, under lights.
Expectedly, Fakhar dominated the 64-run opening stand.New Zealand didn't look like taking a wicket until that point, but Hafeez unwittingly helped them when he stepped too far back to a Lockie Ferguson ball and trod on his stumps.
Zaman's omission is perhaps the most surprising, given that his Test debut yielded two half-centuries (94 & 66) in the last Test that Pakistan played- a thumping 373-run victory against Australia in October in the UAE.
Sohail fell just as Pakistan entered the last 10 overs to an excellent catch in the deep, mistiming a flick off a slower ball and finding George Worker, who ran forward and took a low grab. Hafeez struggled to score quickly, and then trod on his stumps for 19, pushed back in his crease by the extra pace of Lockie Ferguson.
Kane Williamson sat out due to a groin strain with Tom Latham leading the side.
Colin de Grandhomme, Trent Boult and Matt Henry bagged one wicket each. Fakhar, near to his best after gaining confidence from his innings of two nights ago, had his sights on a big innings.
Pakistan left out Imam-ul-Haq on precautionary grounds after he suffered a blow on his helmet in the second match on Friday but his scans were clear. The victor of the match would clinch the three-match series which is tied at 1-1 after the first two games.