Team NZ rounded the first gate fourth, 17s adrift of the leaders, and had moved into third by the second gate, with the British and American boats ahead of them, but were back to fourth at the penultimate gate.
The British sailed a strong race to finish in second, while a bad final gybe saw the Kiwis touchdown and end their campaign early as they were ultimately the last of the competing boats over the line.
Finished second saw Athena Pathway lifted to 37 points, with Orient Express, who did not finish the final race, on 35, and Team NZ finishing on 34.
In Group B, hometown crew Sail Team BCN progressed into the knockout stages alongside the Swedish Challenge and Andoo Team Australia crews, with Canada, Netherlands and Germany eliminated at the end of group stages.
The six remaining teams will now compete in four fleet races, with the top two moving on to contest a one-off match race to determine the regatta winner.
Christopher Reive joined the Herald sports team in 2017, bringing the same versatility to his coverage as he does to his sports viewing habits.