The touring side got its wish to bat first after captain Daniel Vettori won the toss in muggy, cloudy overhead conditions and immediately set out its stall despite losing the early wicket of Brendon McCullum.
Guptill scored 85 and Tim McIntosh 55 not out as New Zealand reached tea on 159 for two, largely taking to heart coach Mark Greatbatch's instructions to get in and stay in on a good batting deck at Rajiv Gandhi International Stadium.
McIntosh had already spent four hours at the crease and was to resume after tea alongside vice-captain Ross Taylor on four.
Guptill was the more fluent of the pair before regretting a decision to play back to left-arm spinner Pragyan Ojha, who trapped him leg before wicket 20 minutes before the break.
It was a rare mistake by Guptill (24), who looked classy during his stay of 203 minutes, hitting nine fours and one six and dominating both the strike and the scoring in a second-wicket stand of 147 with McIntosh.
Fresh from a pair in the drawn first test at Ahmedabad, McIntosh applied himself to register his fifth test half-century, working the ball neatly off his pads interspersed with the occasional square drive.
Guptill's fourth test half-century was easy on the eye as he appreciated a docile pitch and unfurled a series of straight drives against India's attack of two pacemen and two spinners.
The cover drive also served him well and he played his sixth four through that region to raise his century partnership with McIntosh in 149 minutes.
That came shortly after Guptill raised his own 50 by cutting Ojha through point for four, and Indian skipper MS Dhoni was forced on the defensive as he used three boundary riders in a bid to limit Guptill's growing array of strokes.
McCullum's was the only wicket to fall before lunch when he edged fast bowler Shantakumaran Sreesanth to wicketkeeper MS Dhoni in only the fourth over of the innings.
He had made just one scoring shot, a thunderous cover drive for four in the second over from Sreesanth, who generated good pace. McCullum paid a heavy price for a slight error in judgement as he offered Dhoni a regulation catch.
New Zealand ended the first session on 75 for one after the first hour was particularly slow on a surface resembling a billiards table. Just 24 runs came from 11 overs before the drinks break.
McIntoshtook 30 minutes to get off the mark when he square drove left-arm fast bowler Zaheer Khan for two off the last ball of the sixth over.
McIntosh and Guptill looked at ease against the spin of Harbhajan Singh and Ojha, with McIntosh raising their 50 partnership shortly before lunch by hitting Ojha through mid on for four.
Guptill went one better in the next over from Harbhajan when he hit the bowler directly over his head for six as the shackles started to loosen.
New Zealand opted for a seam-based attack, meaning spinner Jeetan Patel made way for Brent Arnel and Tim Southee replaced the injured Hamish Bennett. Batsman Guptill was included at the expense of BJ Watling.
