In reply, New Zealand struggled from the outset, even with an early drop at the rear of the stumps from Jones.
Suzie Bates best-edged the ball to Beaumont off the bowling of Anya Shrubsole, with Down building just 27 just before she was bowled by Sophie Ecclestone.
Nat Sciver dropped Satterthwaite when she was on just two but her reprieve did not previous very long, as the England all-rounder took the capture at the 2nd time of inquiring soon after the Kiwi batter experienced included just 4 additional operates.
Captain Sophie Devine had been dropped on nought but created just 3 runs extra just before she was out lbw, which was reviewed but upheld by the fourth umpire, leaving New Zealand 66 for 5.
Sciver dropped Halliday when she was on 20, just before Shrubsole caught Hayley Jensen to go away the visitors 113 for seven.
The final wickets followed soon following, with Kate Cross and Knight claiming 3 each and every as England secured the victory to acquire the sequence 4-1.