Bairstow was omitted from the Test portion of the tour as a result of his dwindling returns in whites but, in his first innings since then, he anchored a tricky pursuit of 173 as England got home with 11 balls to spare.
Strong winds at the Bert Sutcliffe Oval affected both sides, with England dropping a number of chances in a below-par fielding display, with Anton Devcich (62) and Anaru Kitchen (50no) lifting the hosts to 172 for four.
Pat Brown, Saqib Mahmood and Tom Banton were all given their first outings in England colours as they target international debuts in the T20 series against the Kiwis which starts in Christchurch on Friday.
But it was Bairstow who made the standout impression, crunching six fours and four sixes in an assured performance in front of a smattering of spectators in genteel surroundings.
Banton bludgeoned his second ball in an England shirt high over midwicket for six but he departed for 11, given lbw after playing around one from the menacing Lockie Ferguson, one of five current or former internationals in the home side's line-up.
The New Zealand paceman, who was second highest wicket-taker at the World Cup earlier this year, also had James Vince and Joe Denly caught behind within the space of four balls as England lurched to 51 for three.
England, though, had been ahead of the rate courtesy of some wayward bowling as the wind intensified while Bairstow put on 61 alongside Sam Billings and then an unbroken 66 with Sam Curran, who came in ahead of captain Eoin Morgan.
England required 51 from the final 30 deliveries but Bairstow's three successive sixes off Blake Coburn - the first of which took him to a 36-ball fifty - ensured victory from that point was more or less a foregone conclusion.
It was left to Curran to seal victory, the all-rounder finishing on an unbeaten 28 from 15 balls after smashing the first ball of the penultimate over off Brett Hampton straight down the ground.
Brown earlier went through his assortment of variations while Mahmood proved difficult to get away in the game's infancy, but it was the more familiar names of Chris Jordan and Adil Rashid who prised out Colin Munro and Tim Seifert respectively.
It was a heartening return to action for Rashid following a shoulder injury that has sidelined him since the dramatic World Cup final, the Yorkshire leg-spinner the pick of England's attack with two for 25.
England, though, were guilty of some loose fielding that saw Anaru Kitchen and Anton Devcich each given lives, Mahmood particularly slipshod as he shelled two simple chances at long leg, both times when Brown was bowling.
The pair made use of their reprieves to post half-centuries as New Zealand amassed 79 runs in the final six overs, Kitchen ending the innings with back-to-back sixes to spoil Mahmood's figures as he finished with nought for 35.
