The lead changed nine times in the first fully competitive match-race in a series disrupted in the early rounds by weather vagaries and a spectacular crash involving American Magic.
“That was one for the fans,” British legend Ainslie said.
Ainslie, the most successful sailor in Olympic history, is on record as saying he would willingly trade his Olympic medals - four gold and one silver - to be the first Briton to win the America’s Cup.
But he said there were some tense moments before the Luna Rossa race, which was delayed 80 minutes - first by a wind change forcing a reset of the course, and then a hydraulic fault requiring makeshift repairs on INEOS.
“We were on the back foot. We were missing one of the key settings for the power of the boat so the guys did an awesome job getting us around the track in one piece and getting the win,” Ainslie said, describing the final cross as being “about as close as you want to get”.
With the finish line in sight and Italian entry Luna Rossa holding the right of way, Ainslie managed to keep INEOS in front.
Luna Rossa protested but the race officials ruled Ainslie had maintained the legal distance between the two yachts.
INEOS was written off as the yacht least likely to succeed after failing to win a race in a pre-Christmas shakedown regatta involving the high-tech yachts which fly above the water balanced on foil arms.
But since the competition proper began, it has won all five of its races.
Luna Rossa and American Magic, which is still undergoing repairs, will now race off in a best-of-seven semi-final series with the winner racing INEOS Team UK in a best-of-13 contest.
The winner then faces defenders Team New Zealand from March 6 to 21 for the America’s Cup.