Other New Zealand crew members, including helmsman Peter Burling, were left suspended in the upturned hull of their 50-foot catamaran until support boats could right the craft.
The boat showed signs of damage from the high-speed impact with the waters of Bermuda's Great Sound, where winds were gusting near the maximum allowed for America's Cup racing.
Safety has been a major concern of all the crews and the organisers since the death of British sailor Andrew "Bart" Simpson in San Francisco ahead of the 2013 America's Cup.
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Sailors have helmets, buoyancy aids, oxygen tanks and knives in case their boats get into trouble.
Britain's Ben Ainslie had got the better of New Zealand's Burling in the pre-start to the race, getting a clean run at the start line. The New Zealand crew set off in pursuit but lost control of their catamaran and "pitch-poled" forwards.
The hulls were immersed and the towering "wing" sail tipped over them as it came to a halt. Support boats quickly surrounded the stricken catamaran and the organisers could be heard saying that the crew were all accounted for.
The capsize meant Land Rover BAR won the race, with New Zealand now leading 3-1 in the best-of-nine race series.
"In 30 years of racing it is the most full-on, exhilarating sailing I have ever had," Ainslie was quoted as saying on Land Rover BAR's Twitter account.
"The most important thing is that everyone is okay on Emirates Team New Zealand after their capsize. We look forward to seeing them back on the race course," he added.
Ainslie and Iain Percy, the team manager and tactician on fellow America's Cup challenger Artemis Racing, were both close friends of Simpson and helped set up a charity in his name to promote sailing for young people after his death.
Percy, who was also sailing in Bermuda on Tuesday, was best friends with Simpson and won Olympic gold and silver medals with him in the Star class.
The British crew had suffered equipment failure on Monday when part of their wing controls broke, meaning they had to forfeit two races to their New Zealand opponents.
In the day's other semi-final, SoftBank Team Japan, skippered by New Zealander Dean Barker, took a 3-1 lead over Artemis Racing after winning both their races in the toughest conditions yet of the America's Cup event.
Artemis Racing struggled to control their boat in the strong winds, at one point in the second race sailing off the course completely and incurring a penalty from which they could not recover.
The semi-final winners will go head-to-head to decide who gets to challenge holders Oracle Team USA for the America's Cup itself, starting on June 17. (Reporting by Alexander Smith in London; Editing by Toby Davis and Ken Ferris)
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