Bouchier’s 91 off 56 balls, her second successive half-century, helped England to 177 for three, Charlie Dean taking four wickets as New Zealand were restricted to 130 for seven.
England lost Danni Wyatt, back in the side after playing in the Women’s IPL, early but Alice Capsey and Bouchier – hampered by a quad injury – added 75 in 10 overs.
Captain Heather Knight (21 not out) and Nat Sciver-Brunt (29 not out) smashed 35 off the final 14 balls to set the hosts a daunting target.
That target was made more daunting without captain Suzie Bates, injured in the field, and England struck at regular intervals.
Dean grabbed four for 26, and Brooke Holliday was at the top scoring, with 25 for the hosts.
The win gives England an unassailable 3-1 lead in the five-match series, which concludes in Wellington on Friday.
With the three-match contest tied at 1-1, the hosts were bowled out for a disappointing 116 after being invited to bat first in the decider at Derby.
They never got to grips with Sri Lanka’s array of slower bowlers, with Chamari Athapaththu taking three for 21 and Udeshika Prabodhani and Kavisha Dilhari both claiming two wickets apiece.
Maia Bouchier top scored with 23 while Danielle Gibson added 21 late as England were skittled in the 19th over.
The innings could not have got off to a worse start as Danni Wyatt planted a gentle wide delivery from Inoshi Fernando straight to cover.
The Sri Lankans were celebrating again at the end of the second over when a calamitous mix-up between Bouchier and Alice Capsey saw both batters at the same end, with the latter ran out.
Bouchier and captain Heather Knight did some repair work, sharing a 30-run stand in four overs, but that came to an end when Bouchier holed out to long-on.
Knight (18) and Amy Jones (20) soon followed as England slipped to 72 for five in the 11th over and it looked like they would struggle to get to 100.
But Gibson hit three fours in her 15-ball innings to get them to three figures before a flurry of late wickets saw them fail to see out their overs.
After being dismissed for a duck in the first match on Monday, opener Tammy Beaumont bounced back with a stellar 81-run stand to get England off to a hot start at Seddon Park.
Once Maia Bouchier was caught by Hannah Rowe for 20, England captain Heather Knight set about building an intimidating target alongside Beaumont.
The pair combined for 70 runs before Knight was dismissed by Jess Kerr.
Beaumont was not fazed however, continuing to belt boundaries despite the quick exits of Nat Sciver-Brunt and Alice Capsey.
She lifted England to 158 for five before she was finally dismissed by Rowe.
Amy Jones took the baton from there, contributing 48 from 40 balls as England set a lofty target of 253.
Despite a staunch 57 from Brooke Halliday and a blistering 47 off 48 balls from Izzy Gaze, New Zealand’s batters were unable to threaten England’s score, ultimately being bowled out for 196.
Sciver-Brunt led the way for England’s bowlers with three wickets from her seven overs.
The final match of the series takes place on Sunday.
