Opener Dhawan made 75 not out and his 91-run stand with skipper Virat Kohli helped India overwhelm the revised 156-run target with 14.1 overs to spare -- the Duckworth-Lewis method employed after the setting sun stopped play for a while.
On a high having just won test and ODI series over in Australia, India looked determined to extend their domination across the Tasman Sea as they dismissed their hosts for 157 in 38 overs.
Paceman Mohammed Shami and wristspinners Kuldeep Yadav and Yuzvendra Chahal shared nine wickets among them as New Zealand failed to post a competitive total with only Kane Williamson (64) offering some resistance with the bat.
"150-odd on that kind of wicket was quite an easy total to chase down and it all boils down to the effort of the bowlers," Kohli said.
"The pitch got slower in the second half of the innings but in the first half the spinners cramped the batsmen really well, and got those crucial breakthroughs in the middle overs for us."
Chasing 158 to win, India got off to a steady start before Doug Bracewell dismissed Rohit Sharma (11) to end the 41-run opening stand.
Kohli joined Dhawan in the middle before play came to a halt in extraordinary circumstances as the rays from the setting sun were beaming right into the eyes of the batsmen.
India were set a revised target of 156 from 49 overs when play resumed and the tourists made steady progress with Dhawan and Kohli cruising in the middle.
Kohli, then on 37, was adjudged lbw to Tim Southee but the India captain reviewed it and got the decision overturned after snickometer suggested a faint edge.
Lockie Ferguson eventually dismissed him for 45, a day after the India captain swept the annual International Cricket Council (ICC) awards.
Earlier, Williamson was left to rue his decision to bat in the first ODI of the five-match series at Napier's McLean Park.
Paceman Shami (3-19) made early inroads, dismissing Martin Guptill and Colin Munro in successive overs, bolstering his claim for a place in India's World Cup squad later this year.
Williamson and Ross Taylor (24) embarked on rebuilding the innings but Yadav (4-39) and Chahal (2-43) had other ideas.
Williamson hit seven boundaries in his fluent 64 but wickets kept tumbling at the other end as the spinners struck at regular intervals.
At 107-5 at the mid-innings mark, the hosts' hopes of lasting their full quota of 50 overs rested on Williamson batting through the innings but the Kiwi skipper perished at long-on, playing a premeditated shot against Yadav.
The teams move to Mount Maunganui for the second match on Saturday.
(Reporting by Amlan Chakraborty in New Delhi; editing by ...)
