The Kiwis started the first-to-seven points series with a one-point deficit but were left needing just two more wins to wrest the Cup from the United States of America, with one more race scheduled for Sunday.
It was Spithill and the team bankrolled by Oracle founder Larry Ellison who in 2013 turned an 8-1 deficit against New Zealand into a 9-8 victory and a successful defence of the oldest trophy in global sport. "They sailed very well and won two races".
Despite the lead, we wont get ahead of ourselves because we still know we have a job to do and its still an incredibly tough ask..
Burling, a 26-year-old Olympic gold medallist in 2016, was cool and composed as he "luffed" and trapped the more experienced match-racing specialist Spithill in the "pre-start" of the day's second race, forcing the USA boat to a standstill.
Although the New Zealand team got away, the champions recovered well and fought their way back into the race, finding the speed which had evaded them in previous encounters.
Burling, who at 26 could become the youngest helmsman to hoist sailing's greatest prize, steered his red-and-black, 50-foot foiling catamaran to victories of 12 seconds in Race 7 and 30 seconds in Race 8 on the Great Sound.
Spithill said the powerhouse American-flagged crew - backed by technology from Oracle Corp. and Airbus - continues to make too many mistakes.
Under pressure in the shifty winds, Oracle produced a series of mistakes that further doomed their chances, including a penalty for sailing through the boundary and a splash-down off their foils that saw them slow dramatically.
"That includes me. If the team feel they have a better chance of winning with me on the wheel, I'll be on the wheel, if we feel we have a better chance with me off the wheel, no problem".
Helmsman Peter Burling and Team NZ sit on match point, within one win of lifting the America's Cup off archrivals Oracle Team off Bermuda.
"The plan certainly wasn't to be in this position again, I can assure you of that, but we are here now so it is up to all of us to respond and react".
"It's an incredibly shifty day and we tried to consolidate a little bit halfway up that second beat and let them get a bit closer, but it felt like we had pretty minimal risk that whole race".
England's Princess Anne, center, gestures after the eighth race of America's Cup sailing competition between Oracle Team USA and Emirates Team New Zealand Sunday, June 25, 2017, in Hamilton, Bermuda. "We're really happy with the package they've given us".
Oracle made up 20 seconds down the sixth leg, but Team NZ had more than enough to see them home for a 5-1 scoreline.
Burling appeared to give a friendly wave to the Oracle crew as he sailed alongside and into a controlling position during the prestart of Race 8.
New Zealand snatched back the momentum after the U.S. notched their first win of the series on Saturday.