Counterpart Peter Burling kept his AC50 in the hunt and actually had its nose in front approaching the third mark, when it crossed in front of Team USA, but Spithill managed to squeeze through on the inside and took control on the next run downwind.
On the fifth leg, Team NZ simply miscalculated their course and sailed outside the race boundary, a very basic mistake.
They have looked a class above the other challengers throughout this regatta and yesterday, Burling was excited to see what his team could produce under pressure against the cupholders, with a crucial bonus point at stake.
The outcome should serve as a wake-up call for Team NZ, as the Americans now drop out of the challenger series and the Kiwis square off with a team of their choice in the playoffs.
"There's nothing to hide - we definitely made too many mistakes to win a race today,"
said Burling afterwards. "But there were a lot of positives to come out of it as well.
"We were going really fast and we have to happy with how we did get back into it up that first beat. We were right back in it by the top mark, but there was obviously another little error we made to let him back through.
"That's the positive thing out of our races against Oracle so far - it's been two tiny errors that have let them beat us and we feel like we haven't sailed very good races at all.
"Our boat's plenty quick enough and we just need to sail it well."
Whoever emerges as the America's Cup challengers now start the final series on -1 points, effectively a point behind, and must win eight races to lift the Auld Mug. Team USA need only seven wins to retain it.
In later races, Ben Ainslie Racing dealt Team Japan skipper Dean Barker his third straight loss at the start-line and sailed away for his fourth win of the week, hinting that they had finally found their mojo, after a tough campaign so far.
When these two teams met on opening day, Sir Ben slammed his boat into Japan, suffering a penalty and hull damage that just may have held them back in the days since.
BAR chose to withdraw from their match against Team NZ on Friday (NZT), but had a day off from racing yesterday and teams usually return stronger for that time off the water.
The British continued that trend, with a 13-second victory that consolidated their second position among the challengers.
In their final outing of the regatta, Team France showed why they were heading home, putting up little resistance to Artemis Racing (Sweden), achieving a very low flight-time rating and finishing two minutes 25 seconds behind.
"I think we did a good campaign, not today for sure," said France skipper Franck Cammas. "We enjoy this campaign and we are proud of the job we did with the team over two years.
"I think we achieved a good level at the end, but not enough - we are OK with what we did.
"We learned a lot this time and hope to use this experience for the future. At the next Cup, we want to be on the starting line."
And Team USA further underlined their superiority with a comprehensive victory over BAR in the final race of the qualifying series, winning the start and controlling the contest throughout for a 36-second margin.
Today's schedule
Race 12: Oracle Team USA beat Emirates Team NZ by 29 secs
Race 13: Land Rover BAR beat Softbank Team Japan by 13 secs
Race 14: Groupama Team France v Artemis Racing (Sweden)
Race 15: Land Rover BAR v Oracle Team USA
Standings
Oracle Team USA 8pts
Emirates Team NZ 8pts
Land Rover BAR 6pts
Artemis Racing (Sweden) 5pts
Softbank Team Japan 3pts
Groupama Team France 2pts
