Williams remained at the crease to see his side home, belting three successive fours to ensure Zimbabwe passed UAE's 285 for seven with two overs to spare and ended a seven-match losing streak for Elton Chigumbura's side.
The all-rounder admitted to some nerves during his side's innings as he had recognised the mantle of scoring the 119 runs needed for victory would probably fall to him and fellow southpaw Ervine when they came together at 167-5.
"I could feel it out there," he told reporters in Nelson.
"I tried not to show it. I was just trying to breathe and relax and stick to what we have been doing at training."
Coincidentally it was training that had got the 28-year-old into trouble, again, with Zimbabwe officials late last year.
Williams missed some training sessions due to a family illness, which prompted a confrontation with then coach Stephen Mangongo and being dropped for the Bangladesh tour.
That forced him to consider leaving Zimbabwe altogether to seek a playing future in either South Africa or England.
It would have been the third time he made himself unavailable for the national side after clashes with officials, but Mangongo was sacked in December and strong domestic form saw him brought back into the side.
A poor showing in Zimbabwe's first game of the tournament against South Africa in Hamilton had given him the motivation to succeed on Thursday.
"The previous game against South Africa, I felt flustered at the wicket and it was coming that I was going to get out against them," he said of the eight runs he scored in Sunday's 62-run defeat.
"So I learned from that. Come in, get in, hit the ball down the ground and build an innings then go from there.
"All in all I thought it was a good game to watch and to play."
(Reporting by Greg Stutchbury in Wellington; Editing by John O'Brien)
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