Joy, who had gotten out for 99 in the previous game, hit an unbeaten 103 off 95 balls.
Bangladesh had won the toss and opted to bowl first. New Zealand scored 223 for eight wickets in 50 overs.
Tanzim Hasan Sakib removed New Zealand captain Ollie White for six when the hosts were batting at 10 in 2.5 overs. After adding 18 more runs, New Zealand lost Devan Vishvak thanks to a brilliant fielding effort by Avishek Das to run him out for 10.
However, Fergus Lellman was firm in the middle hitting 116 off 133 with seven fours and five sixes. Jesse Tashkoff (20), Jock McKenzie (10) and Adithya Ashok (14) were the other Kiwi batsmen to reach the double-digit scores.
For Bangladesh, Tanzim, Avishek and Hasan Murad bagged two wickets each while Shoriful Islam took one.
In reply, Bangladesh lost opener Anik Sarker Shatu when the team total was 11. But in the second-wicket stand, Tanzid Hasan and Mahmudul added 90 runs, which laid the foundation for victory.
Tanzid fell for 65 while Mahmudul remained unbeaten for 103. Towhid Hridoy posted an unbeaten 53 as well.
Bangladesh ended on 229 for two in 36.5 overs and sealed the game by eight wickets. They have confirmed the series with two more matches to go.
The last two matches are scheduled for October 9 and 13 at the same venue.