Nat Sciver also starred with bat and ball, taking three wickets as New Zealand were bowled out for 192 with one delivery of their 50-over innings remaining, Brooke Halliday top-scoring with 60.
Despite losing opener Danni Wyatt for a duck and then being reduced to 12-2 when captain Heather Knight fell, England made light work of the chase.
Beaumont and Sciver put on a century-stand for the third wicket before the latter fell to Halliday for 63 off 61 balls, but Amy Jones scored an unbeaten 46 off 45 to see England home with 12.2 overs to spare.
The win, England’s tenth in a row across all formats, gives the tourists an unassailable 2-0 lead ahead of the final game in the series at the same venue on Saturday night.
The two sides will then begin a three-match T0 series in Wellington on Wednesday.