The Supreme Court ruled yesterday that labor unions failing to properly represent a member fired from a job can be forced to pay back wages.

The 5-to-4 decision was an important and potentially costly defeat for the unions, which argued that only an employer could be sued for back pay because the employer does the firing. Suits by members accusing unions of breaching their duty to represent have increased dramatically in the past five years, according to labor lawyers.

Justices dissenting from the court majority predicted that unions now will have to take more cases--and sometimes frivolous cases--to grievance and arbitration in order to avoid responsibility for back pay and that employers could be "insulated" from shouldering the bulk of the costs of their own decisions to terminate an employe.

Justice Lewis F. Powell Jr., writing for the majority, said he believed the ruling would provide an incentive to both employers and unions to engage in arbitration where possible.

The case originated with the dismissal of U.S. Postal Service worker Charles V. Bowen in 1976 after a fight with another employe. Bowen's union, the American Postal Workers Union, AFL-CIO, declined to take his case to arbitration despite recommendations from various union officials that it do so. Bowen then sued both the Postal Service for firing him and the union for failing to represent him properly.

After a trial, a U.S. District Court judge awarded Bowen $52,954 for lost benefits and wages. He said the Postal Service had to pay $22,954 of that amount, and the union owed him $30,000 for increasing his losses by arbitrarily refusing to take his grievance to arbitration. The court said the responsibility for the back wages shifted from the employer to the union at the date the hypothetical arbitration might have occurred had the union taken Bowen's case that far.

The Fourth U.S. Circuit Court of Appeals reversed, saying the union is not responsible for the lost wages. But, reversing the appeals court yesterday, Powell said there was "no unfairness to the union" involved.

"By seeking and acquiring the exclusive right and power to speak for a group of employes, the union assumes a corresponding duty to discharge that responsibility faithfully--a duty which it owes to the employes whom it represents and on which the employer with whom it bargains may rely," Powell wrote.

When the blame for the employe's losses is distributed between the employer and the union, "apportionment" of the damages is fair because it would be "unjust to require the employer to bear the increase in the damages caused by the union's wrongful conduct," he said.

Powell's ruling turned on his interpretation of a 1967 decision in a similar case, Vaca v. Sipes. Justice Byron R. White dissented from much of Powell's decision yesterday in Bowen v. U.S. Postal Service, joined by Justices Thurgood Marshall, Harry A. Blackmun and William H. Rehnquist.