Hridoy finished 51 not out from 27 balls, including two fours and three sixes, having shared a 57-run partnership with Parvez Hossain and another unbeaten 49 stand with Shamim Hossain that guided Bangladesh to the victory.
New Zealand posted a challenging 6-182, after 51 apiece from Dane Cleaver and opener Katene Clarke, and appeared set for victory as their bowlers checked Bangladesh's top-order batters, leaving the hosts 3-77 in the 11th over.
But Hridoy's calculated aggression helped Bangladesh reach 4-183 with 12 balls to spare.
Leg-spinner Ish Sodhi, the only holdover from New Zealand's recent World Cup campaign, led the visitors' early charge with 2-40.
Hridoy then counter-attacked to bring the asking rate under control with support from Parvez Hossain, who made 28 off 14 balls. After his dismissal, Shamim Hossain came in to hit an unbeaten 31 off 13 balls.
Bangladesh captain Litton Das had won the toss and put New Zealand in. Clarke and Cleaver shared an 88-run stand for the second wicket after opener Tim Robinson was run out for a duck in the second over.Â
Legspinner Rishad Hossain, who took 2-32, then removed both of the set batters in consecutive overs to stall the progress.
Bangladesh's pace trio of Shoriful Islam, Tanzim Hasan Sakib and debutant Ripon Mondol were initially wayward but pulled things back after the breakthrough. Tanzim dismissed Bevin Jacobs to leave the visitors under pressure.
Stand-in New Zealand captain Nick Kelly, leading in the absence of injured Tom Latham, steadied the innings before a brief interruption due to bad light.
Following the break, Josh Clarkson provided late impetus with an unbeaten 27 off 14 balls to guide New Zealand to their challenging total.
The three-match series continues Wednesday in Chattogram.
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