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.
However Guptill mixed patience and aggression to good effect, allowing himself quiet spells in the face of tight bowling but also launching the ball back over Ray Price's head whenever the left-arm spinner offered the opportunity.
The 25-year-old had two close calls during his innings, with a strong drive going straight through Price's hands shortly before lunch, while umpire Bruce Oxenford turned down a decent shout for lbw by Jarvis when Guptill was on 77.