Burling said the mistake at the end was his fault.
"We definitely owe our supporters a few beers after that - a few guys on the team reckon they lost a couple of years off their lives, watching that.
"It was my stuff-up, pure and simple, we just missed the lay-line. We were planning on going through the gate, and then carrying on for another 10 seconds and then gybing back to the finish.
"But we just missed that lay-line, we weren't quite ready to gybe back and we hadn't really accelerated out of the gybe. It was just a simple mistake and shows you how tight this racing is - one little mistake and a big lead turns into nothing.
"We were just happy with the way the boys dug really deep, and managed to get that board down and get foiling again to get us to the finish a couple of seconds ahead."
Team New Zealand need just one victory in tomorrow's three races to book a spot in their seventh America's Cup final.