A Tennessee-based hospital chain yesterday won control of Northern Virginia Doctors Hospital, a move supported by the hospital's board but challenged by an Arlington Hospital group that wanted to run the 225-bed facility on a non-profit basis.

After a bitter, two-hour shareholders meeting, Doctors Hospital officials who supported the $19.2 million purchase by Hospital Corporation of America claimed more than 1 million of the hospital's 1.3 million shares, well over the 884,000 needed to approve the sale.

Representatives of the Arlington Hospital Foundation, which claimed 250,000 shares, refused to concede and suggested another outcome was possible. "If I thought we lost, I would say 'We lost,' " said Dr. Kenneth Haggerty, foundation president and chairman.

Haggerty said later that some of the proxies held by Doctors Hospital officials belonged to shareholders who had decided to support the foundation's bid of $20.1 million. "When they heard about us, they switched and voted for us," Haggerty said.

If enough of those shareholders are allowed to revoke earlier proxies and vote for the foundation, the changes could reduce the votes for the Nashville firm to under the two-thirds of the shares it needs for the purchase, he said.

That may not be known until Jan. 17 when a Delaware accounting firm is to issue a final certification of yesterday's vote. Even so Doctors Hospital officials yesterday afternoon were cautiously claiming victory.

They agreed in principle to sell the facility to the chain last summer and leased it to the firm in November, pending the completion of the sale in January 1984. The Arlington Hospital Foundation, which owns the 350-bed Arlington Hospital at 1701 N. George Mason Dr., made a counter offer in December that was rejected almost immediately by Doctors Hospital board chairman Dr. John E. Alexander. Alexander has questioned whether or not the foundation actually had enough money to buy the hospital.

During yesterday's meeting, Haggerty, a dentist and a former chairman of the Arlington County Board, called those charges "an outright lie and distortion of the truth." The foundation has secured a guaranteed loan for the sale, he said.

Haggerty asked stockholders to support the foundation because its plans for the facility at 601 S. Carling Springs Rd. would benefit the Northern Virginia community. He criticized Doctors Hospital officials for supporting the profit-making plan. "As citizens, the Doctors Hospital officials get F minus," he told the stockholders.

Alexander called the chain's plan "an excellent deal financially with the additional attraction that it will greatly benefit the hospital and the community."

William (Gerry) White, the chain's vice president for mergers and acquisitions, said the $3 billion health-care conglomerate believes in "decentralization and local autonomy." He said the firm would place only one representative on the hospital's new board along with local citizens and physicians.

Hospital Corporation owns Circle Terrace Hospital in Alexandria and the Dominion Psychiatric Treatment Center in Falls Church. It has proposed closing both and building a new hospital in western Fairfax County.

White said those plans do not call for closing Doctors Hospital. The company plans to expand the 20-year-old hospital's services with "state-of-the-art" equipment and modernize the building's interior, he said.