Big labor won a stunning organizing victory early yesterday as workers at the huge Newport News Shipbuilding and Dry Dock Co. voted to oust their company-blessed union in favor of the United Steelworkers of America.

Although it drew little national attention, it was a battle of powerful organizations with potentially far-reaching implications for the labor movement in Virginia, the South and the nation: The AFL-CIO's largest union pitted against the combined strength of the world's largest shipyard and its once irrepressible independent union.

The USWA's 9.093-to-7.548 vote victory came as a tonic to the ailing. Organized labor has been suffering from the organizing blahs for years and is losing jobs to lower-cost competition, both from abroad and from nonunion sources at home. Its ranks are dwindling, and it has been losing more representational elections than it wins.

AFL-CIO officials said yesterday they couldn't remember when an industrial union had picked up such a big work force. The National Labor Relations Board, which conducts representational elections, said it was at least one of the biggest in a decade or more.

Although the shipyard campaign was not part of the new union organizing drive in the South, labor officials agreed the outcome here was a good omen and could act as a catalyst for more successful organizing drives.

The USWA's victory over the independent and long-entrenched Peninsula Ship Builders Association was doubly significant in light of a history of repeated failures by AFL-CIO affiliates to crack the armor of the huge shipyard. Newport News is Virginia's largest private employer, a major political power in Richmond and Washington and a mainstay of the Hampton Roads economy.

Four times since the conservative PSA organized the yard in 1939, other unions have tried to topple it, most recently the powerful International Association of Machinists in 1972. All failed, and the prospect was that the 1.4-million-member USWA would fail too.

This was still Virginia, a Southern right-to-work state with a persistent suspicion of national unions and a paternal affection for groups like the PSA, whose new headquarters building here was dedicated by Gov. John N. Dalton shortly before his inauguration last month.

Moreover, the company, along with an anonymous but affluent community group called the "Citizens' Voice", was openly backing the PSA and warning of strikes, job losses and other miseries if the Steelworkers came in.

In this atmosphere, the PSA staged a victory party Tuesday night at its sleek new $1 million headquarters, complete with dance band, drinks and hors d'oeuvres. It quickly turned into wake when word came shortly after midnight that the PSA had finally lost.

It was clear to many that the existence of the PSA, which has only a few hundred members outside the shipyards, is now in doubt. "There's always a tomorrow," said Robert M. Bryant Jr., business manager of the PSA, but several listeners shook heads in doubt.

There was rejoicing at the somewhat scruffier-union hall that Steelworkers' supporters had borrowed.

"Do you realize we beat a system, really beat a system?" exclaimed Pat Nakamura, a weld tester and USWA supporter, in an assessment shared by other revelers at the union hall. "The PSA never called a meeting and said, 'Hey, let's talk.' They sat back and let the company do it for them. If I make a mistake I want to do it myself, and that's what this thing is all about."

The consensus at the union hall was that PSA was defeated by belt-tightening steps that Tenneco, the huge Houston-based conglomerate, took when it bought the shipyard in 1968 and by PSA's lack of militancy in fighting them. "It's like bees to honey," said a former PSA officer who switched to the USWA. "A tough, hardnosed management attracts a tough, hardnosed union.

The PSA's barrage of warnings about the Steelworkers' high strike and job-loss record apparently failed to take hold, despite daily strike reminders in the form of pickets representing 1,200 marine designers who joined the USWA earlier and have been on strike since April.

When the Steelworkers will get a contract is another matter.PSA's Bryant notified members yesterday it will file challenges with the National Labor Relations Board, which ran the election, and there were reports of probable challenges from the company.