When the pair were going well together, England were poised on 267 for one in the 38th over and set to break all sorts of records in the most southerly global venue in world cricket. Then it was down to Williamson and Ross Taylor to steer the innings.
The Black Caps beat England by five wickets in Dunedin to level the ODI series at 2-2.
After two early dismissals, Taylor first stabilized the innings by adding 84 runs with Captain Kane Williamson (45) for the third wicket and then 179 runs with Tom Latham (71) for fourth wickets.
Within three overs of the chase Munro was lbw for a golden duck, needlessly taking New Zealand's review back to the pavilion with him, after Mark Wood pinned him in front of middle - and both openers were gone without a run between them when Martin Guptill tried to hit Chris Woakes over the top but holed out to mid-off.
That's not England's concern - they have ended New Zealand's unbeaten ODI run with two crafty, courageous wins in a row, and can get the job done today.
Ross Taylor celebrates his 19th ODI century.
He combined with Root for a 190-run stand for the second wicket as England looked well on track to push towards a total of 400.
Root himself was dismissed the over after going through to his 11th ODI century, and England were thankful for a flurry of boundaries from Tom Curran (22no) in the final over to take their total up to 335.More news: Secret Service: Male shot himself to death near White House
Talking about his achievement, Taylor said, "It was nice to be there at the end".
However, Colin de Grandhomme (23) came in and with two fours and two sixes from his first six balls, he all but assured the hosts of victory before he was caught at backward point.
With three runs needed from the final over, Henry Nicholls struck a six to secure an impressive win.
He had a life on 74 when Mitchell Santner dropped him at cover. England regained the upper hand with a piece of good fortune, when Santner (41) was run out at the non-striker's end in the 46th over.
Jason Roy struggled to 15 from 26 balls, Jonny Bairstow hit 19 from 39, and Joe Root a much faster 20 from 22 balls. The Kiwi middle-order batsman's swashbuckling innings came off just 147 deliveries and was laced with 17 fours and six huge sixes.
68- Runs scored by England's last eight wickets.
The tone for the England innings had been set by a superb opening partnership of 77 in 10.2 overs between Roy and Bairstow and after Kane Williamson, captaining New Zealand for the 100th time, made a blunder and sent England in to bat.