Zaman remained unbeaten on 106 while captain Babar Azam remained unbeaten on 47 as Pakistan reached 160-1 in the 22nd over when play was stopped due to rain.
Before this match, Pakistan had won three and lost four in seven matches.
Zaman played the first match of this World Cup against Netherlands, but due to poor form and knee injury, he was out of the team.
He returned only in Pakistan’s last game against Bangladesh and scored 81 runs in a seven-wicket win in Kolkata.
Earlier, New Zealand scored 401-6 with the help of Rachin Ravindra’s third World Cup century and captain Kane Williamson’s 95 runs.