Kane Williamson also posted a half-century with 53 off 42 deliveries at Mount Maunganui's Bay Oval.
The pair gave New Zealand a flying start, taking only 28 balls to reach 50 before Nuwan Kulasekara and Jeffrey Vandersay put the brakes on the scoring spree.
The second 50 took 34 deliveries and the score had just ticked over the 100 mark when Guptill was dismissed.
Williamson called for a quick single only for Chamara Kapugedera to throw down the stumps from side on with Guptill well short of the crease.
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Williamson was caught at midwicket off medium pacer Kulasekara, who was the most effective of the Sri Lankan bowlers taking two for 26.
- Selfless Watling -
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Although that gave Zimbabwe some respite, it also brought Ross Taylor and BJ Watling together and the pair picked up where they had left off in the first Test, when they compiled a 253-run partnership.
On Sunday they added an unbroken 193 for the fifth wicket, with Taylor backing up the 173 not out that he scored in the first Test with an unbeaten 124.
"I think it was more important to give ourselves the time to bowl," said Watling. "We had enough runs on the board and we knew it was going to be hard work to take 20 wickets."
That proved to be the case when Zimbabwe's openers shut up shop in the first part of their reply, scoring just 20 runs from the first 19 overs as they successfully saw off the new ball.
"We're going to come up with some plans overnight and hopefully come out and pick up a few wickets early tomorrow," said Watling.
"The wicket is lower and slower than it was in the first Test, and we're going to have to play the long game.