Defending a target of 334, Henry crushed the India top-order on his way to figures of 6-27 as the tourists collapsed to 89 all out as the home side got their first win in the series.
Henry astonishingly took three wickets in the first over of teh rum-chase to leave India on 0-3, before opening bowling partner Kyle Jamieson struck again in the sixth over as the as the visitors were in tatters on 9-4.
Ishan Kishan (27), Axar Patel (21) and Naman Dhir (21) lead a brief recovery for India but the damage had been done already as Henry continued to pulverise the batting unit.
Matthew Fisher also chipped in with 3-31 in seven overs. while Jamieson only conceded 12 runs six overs to completely overpower the visitors.
Earlier, Young struck a composed 125 from 108 deliveries while Tim Seifert hit 58 as the Black Caps were 333 all out in their 50 overs.
The Kiwis would have aimed for much larger total after Young and Seifert out on an 85-run opening stand but failed to build on that platform as India spinner Axar, with figures of 2-39, as the tourists fought back.
The fifth and final ODI of the series will be played at the same venue on Sunday with New Zealand needing another victory to level the series after India had won the first two matches and third game had a no-result due to rain.
New Zealand duo Devon Conway and Rachin Ravindra are doubtful starters for the first Test against India as they recover from injuries, but were named in a 14-man squad for the two-match series.
New Zealand's bowling unit fought hard to defend a low total but India came out on top by four runs (DLS method) in the second ODI in Wellington as the visitors went 2-0 ahead in the five-match series.
New Zealand fast bowler Jacob Duffy believes Virat Kohli remains one of the most difficult batters to contain, after witnessing the Indian star produce a match-winning performance at Eden Park.
Arshdeep Singh took four wickets before Virat Kohli hit 74 as India beat New Zealand by five wickets in a rain-affected first of five ODIs that was played in Auckland on Wednesday.
