England, previously unsuccessful in all four one-day international visits to the Westpac Stadium, got the job done this time to go 2-1 up with two to play after Woakes defied home centurion Kane Williamson by defending 15 in the final over.
Williamson (112no) and Mitchell Santner put the Kiwis back in the see-saw contest after spinners Moeen Ali and Adil Rashid had taken five wickets for 23 runs to reduce them to 103 for six in pursuit of 235 on an awkward surface.
The hosts benefited from a very marginal call when Santner squeezed Rashid to midwicket, where Jason Roy stooped to claim the low catch which would have made it 112 for seven, only for the third umpire to uphold the on-field ‘soft signal’ of not-out because there was no clear evidence the ball had carried.
England got their own critical break, however, when Santner was dismissed - for the first time in the series - in the unluckiest fashion of all, run-out at the non-striker’s end after Woakes’ attempt to catch a straight drive from Williamson was deflected on to the stumps.
The Kiwis still needed another 36 when Santner went in the 46th over - and although Williamson completed his hundred from 133 balls, he could not quite scramble the victory his near lone hand perhaps deserved.
Williamson’s opposite number Morgan was full of praise for Woakes, who kept his cool after Williamson pulled a six off the third ball of the last over.
“Woakes is Mr Reliable,” Morgan told Sky Sports. “He’s a bit of an unsung hero for us with bat and ball.”
In his post-match press conference, the England captain reflected too on the contrasting moments which first saw Santner reprieved and then later dismissed.
“You earn a little bit of luck along the way,” he said. “But Woakesy was trying to catch the ball, and it’s a really unlucky way to get out.”
He sensed Roy had earlier taken a clean catch, but acknowledges the officials reached the only reasonable decision.
“On the TV, it’s not going to look out,” Morgan said. “He said he had his fingers under it, and I believe him.
“(But) there’s no other solution to it. If the umpire is uncertain he has every right to check, and (then) TV just doesn’t look out.”
Morgan agreed that Williamson and Santner appeared to be taking a fluctuating contest away from England again.
“They did ... they played really well,” he said. “It was an outstanding knock from Kane, supported by Santner.”
England’s victory was all the more satisfying for Morgan, because it came on a pitch which did not play to the strengths of his free-scoring team.
“We’re not known as a side that wins games in [those conditions],” he said.
“We fought our way to a competitive total, (and it) was probably quite fortunate that Ben (Stokes) and I had the partnership the other day and were in a good head-space to compare wickets and make a call that it wasn’t a 270 wicket.”
With seven needed from the last three balls, Williamson thought he may just get his team home.
“Woakesy bowled a really nice over - he bowls very good ‘death’,” he said.
“(But) if we’d taken smarter options (earlier), it shouldn’t perhaps have got to that point. It’s very frustrating.
“It was just a shame we weren’t at our best, in the middle with our partnerships ... (and then) we fell at the last hurdle.”