Guptill and Williamson put on 75 for the second wicket at the Queens Sports Club after Black Caps' skipper Ross Taylor won the toss and elected to bat on a flat and lifeless deck.
Brendon McCullum was out early for 14 when he played on to seamer Kyle Jarvis, which brought the two young right-handers to crease and they set about building a strong total for the Kiwis.
Guptill, who was out in the final session for 109 - his second test century - to part-timer Hamilton Masakadza, said it was great to pile on more runs after a good tour so far.
"I'm just riding the wave as it goes,'' he said. "They bowled really well to us today.
"It was a bit of a relief, really. It's been a year-and-a-half since my last test hundred. It's nice to be in the middle and scoring runs. It doesn't happen every day so when you are out there you have to try and make the most of it.''
His previous century came against Bangladesh in Hamilton, when the 25-year-old smashed 189 from No 5 and he said it was frustrating to not be able to kick on to a really big hundred again.
"Just to get there and get out the way I did is pretty disappointing.''
New Zealand picked two debutants for the test - batsman Dean Brownlie and all-rounder Doug Bracewell - and Bracewell will have to get through plenty of work with the ball after coach John Wright picked only a two-prong seam attack.
Veteran Chris Martin is the other paceman in the side, which is filled out by spinners Daniel Vettori and Jeetan Patel.
Ross Taylor ended day one unbeaten on 76 and BJ Watling was on 16 and Guptill said the pitch would break up as the test wore on.
"It's already starting to show some wear and tear,'' he said. "There are already a few balls bouncing through to the keeper after day one.
"We are definitely looking at 450-500. If we can get that, it's going to be very difficult for them to put pressure on us to bat again.''
