Rumman's three for 67 kept the New Zealand total within reach for Pakistan — currently at 4-0 up — as they seek to avoid a 5-0 series whitewash.
Pakistan were competitive in their last outing — a five-wicket loss in Hamilton.
"It's a used pitch and, hopefully, it's better to start with then maybe slows up a little bit," captain Kane Williamson said.
Munro racked up 34 from 24 balls to get the Black Caps out of the blocks before edging to Mohammad Nawaz.
While Munro's departure slowed the run rate, Guptill was content to steadily accumulate.
He had a life on 72 when he slipped over mid-wicket and Faheem Ashraf missed the stumps as the batsman scrambled back to the crease on his hands and knees.
It gave his innings greater urgency and he brought up his 13th ODI century off 125 balls, including 10 fours and a six.
After a frustrating morning, Pakistan's attack enjoyed some late success when they took four wickets for 12 runs.
"We had some good performances and hopefully we'll play well and win this game," skipper Sarfraz Ahmed said.
Guptill was dismissed soon after he reached triple figures and Faheem clean-bowled Ross Taylor to end a threatening knock on 59.
Colin de Grandhomme offered some resistance with an unbeaten 29 off 21 balls but Pakistan will back their chances of reaching the target of 272 in the small boundaries at the Basin Reserve.
New Zealand rested paceman Trent Boult, calling up Matt Henry as a replacement.
Pakistan, on the other hand, made three changes, with Umar Amin opening the batting, Mohammad Nawaz added to the bowling attack, and allrounder Aamer Yamin replacing the injured Shoaib Malik.
Mohammad Amir and Hasan Ali are also not part of the match.
Kane Williamson (Captain), Martin Guptill, Colin Munro, Ross Taylor, Tom Latham, Henry Nicholls, Colin de Grandhomme, Mitchell Santner, Tim Southee, Lockie Ferguson, Matt Henry.
Sarfraz Ahmed (Captain), Umar Amin, Fakhar Zaman, Babar Azam, Haris Sohail, Mohammad Hafeez, Faheem Ashraf, Aamer Yamin, Shadab Khan, Mohammad Nawaz, Rumman Raees.
Chris Brown (NZL), Ruchira Palliyaguruge (SRI)
Richard Illingworth (ENG)
Richie Richardson (WIS)