Hitting the ground running, a sharp Lea Tahuhu (3-25 off 8.3, below), orthodox spinner Morna Nielsen (3-24) and Kasperek (3-39) all hit their mark with the ball, Nielsen unlucky not to pick up a fourth victim after a rare miss off her bowling from Priest when Ekta Bisht offered a thick edge on one.
India's total had fallen well short of their own expectations, yet the White Ferns lost their advantage as they began to lumber with the bat, despite a sloppy Indian fielding performance gifting them some two dozen runs. India reduced the visitors to 95/6 before the imposing Gosawami really stamped her mark by opening the second batting power play with a maiden.
If the hosts were jubilant at having stopped the dangerous Suzie Bates' knock on 28 and picking up fellow opener Rachel Priest for an uncomfortable 19-ball duck, they grabbed a second wind when luck turned against the Ferns, Kate Broadmore run out attempting to steal a run against a well-recovered Poonam Yadav fumble on the boundary, while a promising 26-run partnership for the fifth wicket with Sophie Devine was cut short when Katie Perkins was caught out by a Kaur googly.
Debutante Kasperek, who finished unbeaten on 21, had stood firm against India's rallying spin attack - Sneh Rana picking up 3-26; and had survived a hashed run out chance for India when the Ferns needed to find just a further 38 runs for the win. She took a boundary next ball, and was abetted by number eleven Morna Nielsen who, in a single over, twice edged her way to the boundary off a frustrated Goswami.
But wickets had tumbled too often, and the loss of the influential Sophie Devine in the middle order (caught off Kaur on 24) had been a jarring blow from which the Ferns never quite recovered. India built the wicket pressure until finally Nielsen (9 off 9) was caught, the Ferns dismissed in the 46th over for 125.
While acknowledging her bowling unit's "outstanding" first-up effort after a clearly worthwhile week of acclimatisation, White Ferns captain Suzie Bates was left ruing a lack of intent in a timid chase. "We wanted go out and play our natural shots, but they bowled tightly and we perhaps weren't brave enough with some our shot selections, missing opportunities to push the field back," said Bates.
"Leigh (Kasperek) did a really good job and it was a shame someone couldn't stick with her at the end to give her a good win in her first game. We need to come back out in game two with far more intent."
India pockets two ICC Women's Championship points from the win with two IWC points games remaining on the five-match ODI leg. The two sides meet again at the same venue on Wednesday.