They led Great Britain and the USA through halfway and had clear water with 800m to go. The Dutch pair charged into second late in the race, but the New Zealanders up ahead never looked in doubt.
"We did still have an extra gear if we needed it," said Williams.
"One of the more enjoyable races so really exciting for us…we don't think we've seen the best of our boat yet."
That's how Tom Mackintosh feels after he and Matt MacDonald finished sixth in the A final of the men's pair. They were part of last year's gold-medal winning eight at the Tokyo Olympics so just making the final in a new discipline was an achievement to be proud of, Mackintosh said.
"I'm happy with what we put out today. There's no room for error and you need to be extremely compatible, and that compatibility comes with time."
It has been a time of rebuilding crews and combinations for this Kiwi squad, with four boats competing in B finals on the penultimate day of the championships.
The women's four of Phoebe Spoors, Beth Ross, Davina Waddy and Catherine Layburn were last at the 500m but battled their way through the field to finish second behind Denmark in the B final.
Jackie Kiddle and Rachael Kennedy and Christopher Stockley and Matthew Dunham finished third and fifth respectively in the B final lightweight doubles.
It was a fourth for Stella Clayton-Greene, Kate Haines, Hannah Osborne and Kirstyn Goodger in the women's quad B final.
The men's quad of Jack O'Leary, Stephen Jones, Jamie Hindle-Daniels and Phillip Wilson finished fourth in the C final.
Kiwis in action tonight (NZT)
Emma Twigg, A final women's single sculls, 1.25am
Jordan Parry, A final men's single sculls, 1.44am
Mahe Drysdale, tribute row, after 2am.