Guptill posted his second successive one-day international, the 14th of his career, after top-scoring with 70 in the first match of the three-match series at Dunedin which New Zealand won by 90 runs.
The start of Monday's match was delayed by 35 minutes by rain but no overs were lost and Nicol and Guptill made a circumspect beginning as they studied the pace of the pitch at Cobham Oval which was hosting a one-day international for the first time.
Nicol played out a maiden in the opening over and the New Zealand openers scored only 10 runs from the first five overs as Shingirai Masakadza and Kyle Jarvis bowled a tight line and length.
But Guptill began to impose himself on the match from that point, taking the predominant scoring role as New Zealand reached 49 without loss after 10 overs, steadily increasing its run rate. Guptill reached his 50 from only 44 balls in 48 minutes with six fours and two sixes. He was 65 when New Zealand's 100 came up in the 18th over.
New Zealand promoted Oram in the order, to bat at No. 3 for the first time in more than 10 years and to take advantage of a batting powerplay while Zimbabwe's spinners were operating.
The tactic paid off handsomely as Oram smashed five fours and three sixes on his way to a half century from 23 balls. New Zealand took 44 runs from the powerplay, of which Oram scored 34.
After Oram's dismissal, New Zealand quickly lost Brendon McCullum from 20 and Kane Williamson for four. Nicol immediately assumed responsibility for the innings and became the dominant partner in all remaining partnerships.
In total his innings lasted 199 minutes and 134 ball and he hit 10 fours and six sixes. He hit the sixes down the ground or over mid-wicket, putting one into the neighboring rugby stadium.
He found an eager partner in Latham, the 19-year-old playing only his second one-day international after making his debut in the first match of the series, who scored 48 from 28 balls with five fours and two sixes.
The pair helped New Zealand add 86 from the last five balls of the innings.
Zimbabwe's bowling was wayward and it's fielding woeful it dropped five catches but off-spinner Prosper Utseya saved some face, taking three for 71 from 10 overs.
-AP