Emirates Team New Zealand rebounded nicely from a heart-stopping capsize two days earlier on Bermuda's Great Sound to clinch a spot in the America's Cup challenger finals.
Britain, meanwhile, still hasn't bounced back from its loss in 1851 to the schooner America.
Led by 26-year-old helmsman and 39-year-old skipper-wing trimmer Glenn Ashby, Emirates Team New Zealand won two of three races Thursday against British sailing star Sir Ben Ainslie to win its semifinal series 5-2.
Except for a few hiccups, the Kiwis quickly got back up to speed after Tuesday's dramatic capsize, which threw three sailors into the water and extensively damaged their 50-foot foiling catamaran.
They advance to face the winner between Sweden's Artemis Racing and SoftBank Team Japan. Artemis, led by Olympic gold medalists Nathan Outteridge of Australia and Iain Percy of Britain, beat Team Japan three straight races to take a 4-3 lead in the best-of-nine series, which ends on Friday. Team Japan is skippered by Dean Barker, who was sacked after Team New Zealand blew an 8-1 lead in the 2013 America's Cup and lost to Oracle Team USA.
The winner of the challenger finals, which start Saturday, will face two-time defending champion Oracle Team USA in the 35th America's Cup match starting June 17.
Burling, an Olympic gold and silver medalist, said the shore team ''dug pretty deep'' to get the boat back on the water at close to 100 percent. ''Full credit to them.''
Emirates Team New Zealand, the hard-luck loser in the 2013 America's Cup, overcame an issue with one of its daggerboards at the start and passed the British late in the first race to win by 31 seconds and reach match point.
Ainslie then sailed his best race of the regatta, winning by 20 seconds to stay alive.
But Ainslie made a mistake during the prestart of the next race and Burling calmly steered the Kiwis to a wire-to-wire win of 46 seconds.
Burling said the capsize will be in the back of his mind for a long time. He said the shore team and designers encouraged the sailors to push the boat as hard as they could.
''As the breeze died in the last one, we really let loose,'' he said. ''It was a great day for us to be able to repay the shore crew by getting it done with a day to go.''
At the finish, Ashby and grinder Blair Tuke shook hands with the other three grinders.
As Ainslie steered his boat across the line, he commended the crew for its best day.
The Kiwis then saluted the British crew.
Ainslie, 40, one of the world's most accomplished sailors, hoped to become the first Englishman to hoist the Auld Mug in victory. The British have been trying for 166 years to win back the silver trophy they lost to the schooner America in a race around the Isle of Wight in 1851. They'll have to wait at least two more years to try again.
''We will be back next time and we will be stronger,'' said Ainslie, who added that sponsors Land Rover and 11th Hour Racing have already re-signed for the next campaign.
Ainslie said the Brits weren't able to catch up with established teams.
''We didn't ultimately get that America's Cup home,'' he said. ''We knew it was going to be incredibly tough for the first attempt, but certainly where the team has come from, even in the last couple of months, the performance gains we have made, is a huge credit to everyone in the team.''
Ainslie is the most successful sailor in Olympic history, and he helped Oracle with its incredible rally to defend the Cup in 2013. He was knighted several months after winning his fourth straight Olympic gold medal in home waters in 2012. He also has a silver medal.
SoftBank Team Japan came into Thursday with a 3-1 lead, but took costly penalties in its first and third races of the day, and watched in the second race as Artemis simply sped away.
In the first race, Barker was over the starting line early and had to slow to two lengths behind Artemis to clear the penalty.
In the third race, SoftBank Team Japan didn't give Artemis enough room at the fifth gate mark and was penalized. Outteridge had to do a hard turn to avoid a collision. When Japan slowed to clear the penalty, Artemis sailed way ahead.
Artemis is trying to bounce back from the tragic death of British Olympic star Andrew ''Bart'' Simpson when its 72-foot catamaran broke apart while training on San Francisco Bay in 2013.
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