Although England posted more than 300 for a third successive ODI match for the first time, the hosts failed to use up all their overs as they were bowled out for 302 in 45.2.It left England vulnerable to a New Zealand counter-punch, which was expertly delivered in a national-record third-wicket stand of 206.
As at the Oval on Friday when they put on 121 together, Williamson (118) and Taylor (110) took few chances as they dominated a chase completed with an over to spare and a total of 306-7.
"I think that partnership in the middle was key," Williamson said. "First of all it was important to actually bowl England out today short of their 50 overs. They were on target for a big score and they've played really well again so it was nice to be able to do that and get a total that you could probably break down."
New Zealand captain Brendon McCullum was pleased with his side's improved showing with the ball in Southampton.
"I think last game we were excellent with the bat," McCullum said. "This game we were put under a lot of pressure again, but the way we responded in those last 10 overs was a good sign.
"It shows we've been able to learn in a short space of time and we've got quite a young bowling line-up ourselves so I was really delighted they stuck to their guns and were able to bowl them out inside 50 overs."
England's new commitment to attack at all costs saw Joe Root (54), Morgan (71) and Ben Stokes (68) pile in with decent scores, but losing their last five wickets for 14 runs cost the hosts.
"For a while now we've always played within ourselves and always batted up before the end," Morgan said. "But for a long time we were looking like getting 350-plus and that's exciting to see, particularly when we're trying to change our mentality with the bat.
"Three hundred was certainly well within the game but I think what cost us was Kane and Ross' partnership. They played really well today and all credit to them. We've got a young bowling line-up and we failed to come up with something to break them up."
The next match in the series is on Wednesday.
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