Eastern Airlines and the International Association of Machinists union again veered away from a strike last night, just five hours before a midnight deadline, ending 15 months of negotiations and allaying the anxieties of many spring holiday travelers.

In announcing another tentative agreement at 7 p.m., union negotiator Charles Bryan called it "very fine," and said he would recommend it enthusiastically to his members for ratification in a vote scheduled in about two weeks.

Both sides declined to give details of the agreement until union officials communicated the terms to their membership, perhaps by Friday.

Talks had resumed here Monday after union members rejected by a 3-to-1 ratio what the financially-troubled airline had termed its "final" contract offer.

The rank and file had voted "no," despite emotional appeals by Eastern President Frank Borman. He said a strike at this busy season would be a "catastrophe" for the carrier, which has lost more than $140 million in two years.

Borman said in a statement after yesterday's agreement that Eastern "views with grave concern the increase in wages and wage rates called for over the life of the agreement."

Bryan had contended that Eastern was exaggerating its financial pain as part of bargaining strategy.

In a last-ditch effort to break the deadlock, the talks were moved this week from Miami at the behest of Robert Harris, chairman of the National Mediation Board, which handles labor disputes in transportation industries.

The rejected offer, which Eastern produced 12 minutes before a March 13 strike deadline, would have raised wages by 32 percent over three years. The union had complained about the amount and the timing of the money provisions.

The new pact would cover the period from Jan. 1, 1982, to Dec. 31, 1984.

Top pay for the union's 13,000 mechanics, baggage handlers and other ground workers at Eastern is $13.15 per hour