And it's New Zealand's third win batting second against the Indians in India.
Lefthander Latham, slipping into his new middle order role, scored an unbeaten 103 off 102 balls - having done 50 steamy overs of wicketkeeping first, while New Zealand's senior batsman Taylor was out for 95 with the scores level.
Latham's fourth ODI ton was the second of the match, following an outstanding 121 from India's captain Virat Kohli, his fourth against New Zealnd and 31st overall.
That seemed to have been enough to put India in the driving seat.
However New Zealand had other ideas in what captain Kane Williamson called a "brilliant" performance.
"That's one of the best chases that I've seen, certainly in the time I've been a Black Cap," he added.
Martin Guptill and Colin Munro put on 48 for the first wicket. Captain Kane Williamson missed out and when Guptill departed for 32 at 80, the game was in the balance.
But Taylor and Latham both made centuries during last Friday morning's warmup against an Indian President's XI and they produced quality performances.
Taylor might have been run out on other days at both 40 and 56 but this was his, and New Zealand's day.
They swept well and worked the ball about effectively and got a terrific reward.
In sticky, humid conditions, the match began encouragingly for New Zealand, through the efforts of left armer Trent Boult.
He had warmed up for the internationals in India by taking five for 38 in the first of two leadup games against an Indian Presidents XI and was right on song from the start of the Indian innings.
He dismissed both openers Shikhar Dhawan and Rohit Sharma with fine swinging deliveries.
Dhawan was caught behind wafting at a ball which swung away from the lefthander; Sharma played an injudicious heave but the ball swung in between bat and pad.
Boult's first five-over spell produced an outstanding two for seven.
Left arm spinner Mitchell Santner dropped onto a good line, found some spin, and induced a return catch from the unimpressive Kedar Jadav, but then made a huge blunder which had significant repercussions for New Zealand.
Fielding at shortish cover, Santner spilled a straightforward catch from Kohli on 29 off seamer Colin de Grandhomme. The ball was driven uppishly, and was evidence that the pitch had a holding element in it, leading to batsmen often mistiming their front foot shots.
It went through Santner's hands. Not long after, Kohli, in his 200th ODI, was planting fast bowler Adam Milne to the long on boundary 46th ODI 50; some time later he was gently pulling Tim Southee behind square for his 100th run.
It was his 31st ODI century - only Sachin Tendulkar's 49 are in front of the Indian skipper - his fourth against New Zealand, and fifth in 2017 and a terrific display of fitness and skill.
New Zealand managed to break a threatening stand between Kohli and Dinesh Karthik at 73 when Karthik misjudged a hook at Southee to be caught, after a juggle, by Munro.
MS Dhoni and Hardik Pandya made handy contributions before both falling to Boult, the latter to a fine, running catch off a skier by Williamson.
Boult's display, four for 35 off 10 overs in gruelling conditions, was top class; Santner, save his final over which cost 10, splendidly parsimonious. Southee took late punishment but finished with three wickets.
"We though 275 plus was good on that wicket but New Zealand batted really well in the second half and Ross and Tom were outstanding," an admiring Kohli said.
"They deserved to win. Their partnership was outstanding. When you get a 200-run partnership in ODI cricket, more often than not you end up on the winning side."
Williamson was elated.
"The way we set the tone with the new ball at the start of the day was outstanding from our front two bowlers (Boult and Southee) and we struck at it well throughout that innings," he said.
"That 200-run stand was a special, special partnership."
The second match in the three-game series is in Pune on Wednesday night (NZT).
