Emirates Team New Zealand beat Sweden's Artemis Racing by only half-a-second to go 4-2 up in the best-of-nine America's Cup challenger play-off final.
Trailing 2-1 from Saturday, the Swedish team took Sunday's first race in Bermuda by 15 seconds to level matters.
New Zealand came from behind to win the next two, the most dramatic of which came via a sprint finish in the last.
Artemis protested over the course steered by New Zealand but the umpire ruled there had been no fault.
The final will conclude on Monday.
Emirates Team New Zealand have six Olympians in their squad, while Artemis have a total of eight, including Britain's Iain Percy, who won two golds and a silver across three Olympics from 2000 to 2012.
Holders Oracle Team USA await the winners of the challenger final in the America's Cup.
The first to seven points wins the America's Cup, or the Auld Mug as the trophy is known, with a possible 13 races to be sailed on 17-18 and 24-27 June.
The America's Cup, the oldest competition in international sport, was first raced in 1851 around the Isle of Wight and has been won by only four nations.