On a wicket that did not appear to hold many demons, De Grandhomme finished with one for 24 off 10 overs with his medium pacers.
With the series level at one-all after the first two games, New Zealand elected to bowl after winning the toss and took immediate control.
Most of the England batsmen reached double figures but they were unable to dominate with captain Eoin Morgan top scoring with 48.
Jos Buttler managed to attack the bowling until Ish Sodhi, the most successful of the New Zealand bowlers with three wickets, had him caught behind for 29 off 23 deliveries.
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New Zealand introduced the spin of Mitch Santner in the 11th over, with England 36 for one, and on his fifth ball Joe Root had a life when he drove a long hop to midwicket where Williamson dropped a one-handed catch attempt.
But Root was to add just 11 more runs before he charged at de Grandhomme and only managed to loft the ball to Sodhi at mid-off.
The tourists were then three for 68 in the 17th over and the run rate slowed when Ben Stokes joined Eoin Morgan. They managed only five runs in their first three overs together.
Stokes, the England hero when they won the second ODI three days ago, was sadly out of sorts with nine runs off the first 24 deliveries he faced, while Morgan picked up ones, twos and the occasional boundary at the other end.
As England moved to 166 for four with 10 overs to face, Stokes' patience ran out and when he tried to pick up the pace, he lifted Sodhi to long off and was gone for 38 off 73 balls.
Jos Buttler refused to be confined but could only manage 29, while Moeen Ali cracked 23 before he was the first of three tail enders to be run out in a late search for runs.
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