Latham (110 not out) scored his maiden ODI ton and was virtually matched by Guptill (116 not out) as the tourists easily chased down their victory target of 236 to level the three-match series at 1-1.
Zimbabwe won the toss and elected to bat, but despite an eye-catching unbeaten century from Sikandar Raza, their 235 for nine off 50 overs never looked enough.
New Zealand raced past the hosts' total without losing a wicket and with 46 balls to spare.
The opening stand is New Zealand's second-highest in ODI matches and is the second time that the Black Caps have beaten Zimbabwe by the maximum 10-wicket margin - Guptill also helping them home at the World Cup in India four years ago.
Sikandar Raza (100 not out off 95 balls) provided the lone resistance in the home innings as he reached his third ODI ton and took the record for the highest score from a Zimbabwe player batting at number seven or lower in 50-over international cricket.
He also featured in a Zimbabwe record ninth-wicket stand of 89 with Tinashe Panyangara before the latter was run out for a career-best 33.
New Zealand leg-break bowler Ish Sodhi, who made his ODI debut in the first game of the series on Sunday, returned the best figures for the tourists with three for 38 from his 10 overs.
The series decider will be played at the same venue on Friday.
(Reporting by Nick Said; Editing by Neville Dalton)
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