England captain Charlotte Edwards chose to field first after winning the toss and Sara McGlashan (64) and Nicola Browne (38 not out) made the biggest contributions in a score of 206 for eight.
Isa Guha claimed exemplary figures of 2-27 and Holly Colvin was not far behind with 3-31.
In reply Morgan’s knock was highly significant and she shared a 91-run stand with Jenny Gunn (27), Nicki Shaw (24 not out) also provided crucial runs.
Shaw hit the penultimate ball of the game for four as England reached 208-7.
The series had already been one by the visitors but the final score was 3-2 to New Zealand.