Eastern Airlines tentatively agreed to be acquired by Texas Air Corp. at the end of a tense, emotional meeting early yesterday after a key labor official refused to grant further wage concessions unless Eastern's top management were removed.

The purchase of Eastern by Texas Air, for a price estimated at more than $600 million, will create the nation's largest airline, if it is approved by shareholders and the Department of Transportation and passes other potential legal hurdles. There may be antitrust questions raised about combining Eastern with New York Air, owned by Texas Air, because they are leading competitors in the Washington-New York-Boston air corridor.

The proposed acquisition of Eastern also represents another victory for Frank Lorenzo, president of Texas Air, which also owns Continental Airlines. Lorenzo has taken advantage of airline deregulation to make his low-cost, nonunion airlines formidable challengers to older airlines, including Eastern.

An Eastern spokesman said yesterday that the company intends to maintain normal operations while awaiting approval of Lorenzo's offer. See related stories, Page F1.

Eastern apparently will have the cooperation of its pilots union, which agreed to new labor cost concessions early yesterday after marathon negotiations. The negotiations were going on not far from Eastern's Miami headquarters, where the airline's directors were meeting on Lorenzo's offer. The pilots approved a 20 percent pay cut and other concessions in benefits and work rules, with the promise of employe bonuses in 1988 if Eastern is profitable next year.

The pilots union had set a strike deadline for midnight Tuesday, but the new contract removes that possibility, a union spokesman said. "I think we have a valid contract, and the pilots are going to work to the letter of the law of that contract," said Don Skiados of the Air Line Pilots Association.

But it was Eastern's bitter relations with another union -- the International Association of Machinists and Aerospace Workers -- that forced the sale of Eastern to Lorenzo's company, union and company officials agreed.

The climax of Eastern's board meeting early yesterday morning came in a showdown between Eastern Chairman Frank Borman and Charles Bryan, the IAM official who represents Eastern's machinists and mechanics and sits on Eastern's board.

According to accounts confirmed by IAM officials, Bryan said the machinists would agree to a 15 percent wage cut as part of Eastern's overall cost-reduction plan -- but only if the directors replaced Borman and other top Eastern officials, whom the machinists accuse of mismanaging the airline.

Eastern's directors rejected Bryan's proposal. But that meant Bryan would not agree to further labor cost reductions by the machinists union. Without the cooperation of the machinists, Eastern could not satisfy the demands of its lenders, who had called for labor-cost concessions by all three of Eastern's major unions -- the pilots, flight attendants and machinists.

The lenders, headed by Chase Manhattan Bank, are owed $2.5 billion by Eastern and were prepared to put the loans into technical default if the cost reductions were not in place by Friday.

The lenders' ultimatum confronted Eastern's directors with a painful choice, one source said. If they did nothing, Eastern might be forced into a bankruptcy reorganization. Or they could accept Lorenzo's offer to acquire Eastern for about $10 a share of Eastern common stock, including $6.25 a share in cash and $3.75 in Eastern subordinated debentures, bearing 13 percent interest and guaranteed by Texas Air.

The directors chose the latter course, and at 2:51 a.m., according to one observer's notes, Borman stepped out of the directors' meeting to announce to company officials and others involved in the negotiations that the company had been sold.

"It's nothing that any of us wanted to see happen," said one source on the company side in the negotiations. "It's really frustrating. We had to get the costs out. Everybody knew this. [But] no amount of persuasion would move Charlie Bryan. One guy held the fate of 41,000 employes. . . .

"You'd like to die a noble death, you don't want to kill yourself slipping in the bathtub. That's what we did here," the source said.

From the machinists' standpoint, however, Borman and Eastern's top management had used up their credibility during the airline's struggles to regain profitability following deregulation. They contended that further concessions to Borman would be throwing good money after bad.

The machinists, pilots and flight attendants unions contended that Eastern under Borman embarked on a poorly planned strategy to cope with airline deregulation. Eastern saddled itself with one of the heaviest debt burdens in the industry by purchasing a large fleet of new fuel-efficient airliners, only to see declining jet-fuel prices undermine the advantages of the strategy, union officials said.

"Borman's head has to be part of the deal," machinists union President William W. Winpisinger said in a recent interview.

The machinists' role in insisting on Borman's ouster, ending up with Lorenzo as the apparent winner, is an ironic reversal of the union's role in the 1985 attempt to take over Trans World Airlines. In that case, the machinists union injected itself into the takeover machinations with the goal of preventing a Lorenzo takeover. The machinists at TWA offered substantial concessions to corporate raider Carl C. Icahn in a successful attempt to block Lorenzo.

Lorenzo's plans for Eastern and its management weren't disclosed.

Winpisinger said yesterday he considers Lorenzo's offer to be a "low-ball" bid that understates Eastern's value as a going concern and may face legal challenges from stockholders.

Company sources said that Borman attempted to find other buyers for Eastern, in and out of the airline industry. "With the debt we had and labor rates, we were not very attractive," one source said.

Lorenzo's first move, should he succeed in taking control of Eastern, probably will be to demand further wage and benefit concessions, said John V. Pincavage, an airline industry analyst with Paine Webber.

Eastern's average wages of $112,535 for pilots, $41,879 for mechanics and $30,464 for flight attendants are higher than those of most of its key competitors.

Pincavage said Eastern's labor costs and total operating costs both are considerably above the industry average. "It is a combination of factors" that created Eastern's precarious situation, he said. "But when one looks for solutions, the easiest place to attack is the labor expenses."