That list included the Austrian pair of Benjamin Bildstein and David Hussl who started the day in third and slipped to ninth overall, as well as Great Britain's Dylan Fletcher-Scott and Stuart Bithell who were 21st in their last race and are fourth overall.
In fact, Burling and Tuke now hold a handy 23-advantage over France's Lucas Rual and Emile Amoros in third.
Logan Dunning Beck and Oscar Gunn lost some ground, slipping from sixth to eighth with three middling scores, but the third Kiwi combination of Isaac McHardie and William McKenzie climbed from 22nd to 14th overall with three solid races.
It was another frustrating day for Alex Maloney and Molly Meech in the 49erFX, with the Olympic silver medallists opening up with a 20th before finishing ninth and fourth in the other two races.
Olympic champions Martine Grael and Kahena Kunze, of Brazil, hold an 11-point lead over reigning world champions Annemiek Bekkering and Annette Duetz, of the Netherlands.
Although Maloney and Meech are ninth, they're only 21 points off third.
"We're feeling a bit frustrated with our performance but we still believe anything can happen and we can still fight our way back up," Maloney said.
"I think we are going to go out there punchy-as [tomorrow] and really try to get off the start line to give ourselves the best opportunity to win some races because we know we can do that."
Micah Wilkinson and Erica Dawson proved that when they won the final race of the day in the Nacra 17 fleet and are now 17th overall, three points behind fellow Kiwis Liv Mackay and Jason Saunders in 15th.
All three of the New Zealand Nacra 17 crews in gold fleet are new combinations and all have had their moments this week and the bullet was the first at international level for Wilkinson and Dawson. "It was nice to finally execute," Wilkinson said.