"All guys are accounted for," Burling assured after the scary capsize.
"We are just trying to right the boat."
Immediately after Team New Zealand went over, Ainslie ordered his support craft to go back and help his opponents.
Speaking to media after the incident, Ainslie described the scenes as something he'd "never experienced"
"We had a chat about it this morning with our support team - we had that discussion that if something goes wrong with the other boat, we'd stop and make sure we give every assistance we can," said Ainslie.
"Thank God, it sounds like everyone's OK ... that's the most important thing in these situations.
"To be honest, this is the first time we've sailed this boat in this much wind, so we're learning as we go. It's just absolutely full-on, it's mindblowing."
The race was black-flagged, gifting Sir Ben Ainslie the win and taking the scoreline to 3-1, in Team New Zealand's favour.
Earlier that day, the Kiwis almost didn't make the start-line for their opening race, after suffering damage to their wing in the build-up and returning to shore to hurriedly install a replacement part.
In winds threatening the average upper limit of 24 knots, they were on the water, preparing for their third semifinal race against BAR, when they appeared to suffer damage to their wing.
Emirates Team New Zealand worked feverishly to install their second wing in time for the start and were assisted.
Fortunately, the mishaps didn't get in the way of an ultimate Kiwi victory with Team New Zealand going on to face Oracle Team USA in the final and claim the Auld Mug.