The victory puts England 1-0 up in the three-match series.
England, back in action in the ODI arena for the first time since playing Pakistan in December 2019, lost the toss.
New Zealand elected to bat, but despite being deprived of Anya Shrubsole's services – sidelined from the tour with a knee injury – England were soon on the front foot after Tash Farrant and Katherine Brunt both struck inside the opening 10 overs.
Hayley Jensen provided New Zealand with some hope after she claimed her first maiden ODI half-century, but her dismissal by Sarah Glenn left the hosts on a precarious 94 for four.
In reply, Wyatt's wicket fell in the eighth over after she registered 17.
But Beaumont and Knight steadied the ship, with the former making 50 from 67 balls – her 10th ODI half-century – before she was caught behind off Lea Tahuhu's delivery.
Knight then reached her 20th ODI 50 in 58 balls, with Nat Sciver (21no) hitting the match-winning boundary in a crushing triumph for the tourists.
The sides will meet in Dunedin on Friday with England bidding to take an unassailable 2-0 lead.