In the end, the New York Yacht Club did it with style.

At noon today on the sun-splashed portico of William K. Vanderbilt's seaside mansion, Marble House, the club turned over the most prestigious prize in yachting, the America's Cup, to a band of merry Australians.

The NYYC initially proposed concluding this acrimonious summer by transferring the silver mug at club headquarters in Manhattan, thus providing the winners, who came from across the world to compete, one final travel indignity. The Aussies responded by saying they might send a messenger. But last night the club relented and arranged for a proper ceremony here and today the historic exchange was performed with all the grace and formality it deserved.

On Monday the Aussies, riding spectacular white Australia II with its winged keel, completed what they came here calling "Mission Impossible." They ended the world's longest winning streak, the NYYC's 132-year hold on the cup, by beating Liberty, 4-3, in the first-ever cup series to go the seven-race limit.

The Australians weathered a steely sailing performance by Liberty skipper Dennis Conner, who gave them a battle to the end even though his boat was outclassed.

They also weathered a summer-long barrage of legal attacks by the NYYC, which maintained the wings that gave Australia her speed were a "trick" and an illegal "peculiarity." The club sought to discredit the inventor, Ben Lexcen, by saying he had help from Dutch scientists.

But today the acrimony evaporated in a sea breeze high over the bluffs as Commodore Bob Stone, wearing the dress blue blazer of the NYYC, presented the ornate, 2 1/2-foot-tall mug to Commodore Peter Dalziell of the Royal Perth Yacht Club, in dress whites.

"There is no country we'd rather see get it," said Stone graciously. Dalziell responded that the cup "will have pride of place in our clubhouse," and added, "We'll welcome all challengers in the summer of '87 (January through March, the Australian summer)."

The 11 Aussie sailors and 20 support personnel of the Australia II team hoisted the cup in triumph.

They should be happy, because this moment very easily might not have been. They were a lucky bunch to win the cup, coming from behind in the next-to-last leg of the last and deciding race to win by a scant 41 seconds in one of the two best contests of the series. "If we'd known what we were doing," conceded tactician Hugh Treharne, "we should have won this a week ago."

They lost the first two races to gear breakdowns and one to a superb tactical performance by Conner, who sailed a slower boat faster by picking the wind shifts and playing all angles to go up, 3-1, and seemingly put the cup out of reach.

But Australia was too fast. Even though Conner won all the starts in the last three races, he couldn't stop the sleek white boat from marching over him each time.

Liberty crewman Jon Wright and a crowd of other curious people stood at Australia II's dock early this morning getting a long-awaited look at the mystery keel, which was shrouded all summer so no competitor could copy it.

After winning, the Aussies let the world see, and this morning the yacht was still hanging from her lift at the dock, her curious underbody open to public view.

Curious it is. "It's like a regular keel only turned upside down," designer Lexcen explained. The keel is about twice as long on the bottom as it is on the top, an inverted V that is exactly opposite convention. The wings on the bottom are lead, six feet across and slanted down at about a 20-degree angle.

The effect is to put a mass of weight low. The rest of the boat is unusually light, but with the wings and heavy keel-bottom she has extraordinary stability and stands up, even in a blow. Thus Australia II has the best of all worlds--lightness for speed in gentle breezes; stability in heavy air. She was better than Liberty across the board.

Said Wright, "I guess if you have to get beaten, it's better to have it be by something wild like this than something normal."