With 15 needed off the final over, the New Zealand skipper, who went past his century struck a six in the third delivery and needed another maximum in the final delivery but Woakes bowled it full and wide only for Williamson to let it untouched as England completed a four-run victory.
New Zealand, boosted by the return of Kane Williamson from a hamstring niggle, will be confident of securing the 235-run target.
Ben Stokes did not hit his first boundary until his 53rd delivery but England knew the pitch meant New Zealand's run chase would be hard.
Needing a four to draw or six to win off the last ball, Williamson was unable to make clean contact with a Chris Woakes yorker as the tourists celebrated a gritty win on a hard Wellington pitch. It is located in New Zealand.
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New Zealand appeared to have the game in their hands at 80 for one in the 18th over, before Ali and Rashid turned the match with five wickets for 23 runs in a 41-ball burst.
He also saw a chunk of his now unsponsored bat broken off by a ball from the strictly medium-paced Colin de Grandhomme, who returned old-fashioned miserly figures of one for 24 off his 10 overs.
When the teams met in a T20 on the same ground last month, that was the case, the pitch containing more runs, and producing a far better contest, than looked likely. The team England is now travelling in New Zealand and as per the schedule, they are playing an ODI series against the Black Caps.
New Zealand's middle order then failed to deal with England's spin duo - Ali having Mark Chapman (8) caught at backward point, pinning Tom Latham (0) lbw for a golden duck on review and then having De Grandhomme (3) pouched at long-on.
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"Brilliant game of cricket", England captain Eoin Morgan said.
Ish Sodhi was more expensive with his leg breaks, but still claimed three wickets for 53, while there were three late run outs as England pushed for runs at the end of their innings. "We aren't known for that, we're known as a side aggressive with the bat".
England have played four previous ODIs at the Westpac, but are yet to win one - bowled out for 89, 130, and 123 respectively, and then making 309 for 6, before being beaten by nine wickets by Sri Lanka.
The fourth ODI, which will be a deciding one, will be held at University Oval in Dunedin on March 7.
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