Things had been going slowly the tourists' way when Guptill, on 97 and looking for his first ton against a side other than Bangladesh or Zimbabwe, slogged Sunil Narine to the grateful waiting Narsingh Deonarine just three overs before the end of the session.
It was Narine's third wicket and put the hosts back on an even keel after they had earlier looked to be toiling at the Sir Vivian Richards Stadium after Kiwi captain Ross Taylor had won the toss.
Guptill had already had a scare when a review got him out of jail when he appeared to have been trapped lbw.
Taylor made 45 but was bowled by Narine, who ended the day with three for 73.
But it was the demise of Guptill which hit the tourists as he was replaced by Kane Williamson, who had made two at the close with debutant and nightwatchman Neil Wagner on four.
The match saw top-order batsman Chris Gayle return to the West Indies Test line-up for the first time since December 2010.
Gayle has been absent from the Test side due to a standoff between himself and the West Indies Cricket officials board sparked by critical comments he made about officials in a radio interview after a sponsorship row.
In a relatively sedate opening the Black Caps, beaten in the preceding one-day series, settled down as Daniel Flynn and Guptill moved the score along.
Flynn had a scare when Kemar Roach made an early leg-before appeal in a slow start as six overs brought only as many runs.
But the pace then quickened as Flynn hit two boundaries off Darren Sammy before Guptill survived a caught-behind appeal.
Flynn hit another boundary off Sammy in the 18th over to bring the score up to 50 before Guptill slogged Sunil Narine for six.
A review then went against the hosts as Guptill was given not out lbw to Sammy following an inside edge.
A flurry of maidens held up the visitors either side of lunch before Flynn smashed Narine to the ropes while Guptill twice did the same to Ravi Rampaul.
As the 100 mark beckoned Narine landed his first Test wicket as Flynn miscued an effort to Kieran Powell at point before Guptill secured his half-century in driving Roach for another boundary.
New partner Brendon McCullum survived a review for lbw but then was out driving to Narsingh Deonarine at mid-off having made 25.
The West Indies have dominated the tourists so far this summer, taking the Twenty20 series 2-0 in which Gayle was awarded man of the series, and the ODI series 4-1 in which Gayle made an aggressive century and half-century.