However, a nosedive by the French team in the penultimate leg lead to a nervy conclusion as both teams raced for the finish line.
Skipper of Sweden Nathan Outteridge is disconsolate at the end of the race.
After the first day of round-robin qualifiers Team USA were tied atop the standings with Britain's Land Rover BAR, both on three points. The team is made up of some of the best British and global sailors, designers, builders and racing support.
There is a saying in Bermuda that everyone has a boat but the only eyes will be on BAR, Team Oracle USA and the rest of the America's Cup fleet. They beat BAR by 53 seconds before crashing to a 2min 34sec loss to Team Japan.
"We hold ourselves to high standards so we're not completely satisfied", he said. "So I can be proud of our team, and where we have come from and the potential we have to move forwards, this is hugely positive for the team", he added.
Groupama Team France had appeared to struggle to keep their boat on its foils during some manoeuvres against defenders Oracle Team USA on Saturday, with their hulls occasionally ploughing into the water and losing them precious time. "We will approach every race trying to win".
A subsequent review by the umpires saw them admit they got things wrong.
Land Rover BAR, who won the day's fourth race with a narrow 11-second victory over Sweden's more fancied Artemis Racing, ended on a low after suffering damage before the start in a collision with SoftBank Team Japan.
With Emirates Team New Zealand coming hot on starboard to the mark and Artemis on port. Tacking and jibing incredibly smoothly, the Kiwis chased down their rivals before overhauling them heading for gate 5.
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"However, I'm extremely proud of the way the whole team regrouped from that defeat and fixed everything in an nearly ideal race against Oracle Team USA".
In other races, Artemis - whose stock has risen with some impressive practice performances this month - defeated Team Japan by 13 seconds.
All six boats will race against each other twice, in newly designed boats, and the top four will progress into the challenger round. Oracle Team USA will skip this stage and head right to the finals. Four years ago, Team New Zealand reached match point against Oracle on San Francisco Bay before the American team, owned by software billionaire Larry Ellison, won eight straight races to cap one of the greatest comebacks in sports. So they punctured our hull from underneath, and we have done quite a lot of damage to the hull.
But returning to Land Rover BAR's first race against pre-race race favourites Artemis Racing, Ainslie's crew dominated. The case-back also bears Sir Ben Ainslie's lucky number, three, which has featured on all his winning boats.
"When you look at the conditions, it's no surprise at all that either team could have been a long way ahead", he said.
A year earlier he was disqualified at the World Championships, jumping off his boat and swimming to remonstrate with a watching craft he claimed got too close. I am excited to think that we may see these types of lead changes for the entire regatta!
Artemis became the first team to beat Oracle Team USA on Sunday in the America's Cup qualifying event which is taking place in Bermuda this week.
'Between him and I we need to work out quickly how we take over the responsibilities throughout the race on these key decisions.