Guptill made the most of a flat pitch to hit 109, while captain Ross Taylor [ Images ] made an unbeaten half-century as the Black Caps closed day one on 275 for three.
Zimbabwe's bowlers found the going tough on a wicket which offered little assistance, but could have dismissed both Taylor and BJ Watling in the final half hour of the day were it not for a couple of dropped catches.
Taylor, who finished the day unbeaten on 76, was fortunate to see his thin edge down the leg side off Chris Mpofu's bowling dropped by the wicketkeeper Regis Chakabva, while Watling edged a delivery from Kyle Jarvis past first
slip just a few overs later.
The rest of the day was often short on entertainment as New Zealand marched methodically towards a big total and
Zimbabwe did their best to contain them.