The pair's first-wicket partnership produced 96 runs before Axar Patel dismissed Latham, who hit 39 runs off 40 balls before returning to the pavilion.
Guptill stormed to a half-century and was eventually taken out by Hardik Pandya after scoring 72 runs off 84 deliveries.
Captain Kane Williamson fell nine runs short of 50, while the remainder of the batting order failed to surpass 35 runs as New Zealand posted 260-7 in 50 overs.
In reply, India suffered an early wobble as Rohit Sharma was dismissed for 11 off the bowling of Tim Southee, but Ajinkya Rahane and Virat Kohli kept the attack ticking before the latter was taken out by Ish Sodhi.
Rahane ended his innings with a knock of 57, but his teammates struggled to match him as the hosts ended up requiring 23 runs with just one wicket and 12 balls remaining.