Pan American World Airways won a round in court yesterday in its continuing fight with the Civil Aeronautics Board for a domestic route.

The United States Court of Appeals here told the CAB that "fundamental fairness" requires it to reconsider its 1976 decision granting Western Air Lines, and not Pan Am, the authority to fly between Miami and Los Angeles in competition with National Airlines.

When the CAB made its decision in the nine-year-old case last year, it accepted an administrative law judge's 1973 determination that the Miami-Los Angeles route was large enough and, in fact, needed competitive service, but rejected his recommendation that Pan Am should be awarded the route.

In its appeal to the court, Pan Am charged that the CAB, in making its decision, unfairly took into account events occurring during the three-year interval between the closing of the record in the case and its decision.

The court was persuaded. "As Pan American has emphasized, the complaint focuses not so much on staleness as on the selective character of the updating voluntarily undertaken by the board," the three-judge panel said in an opinion by Judge Carl McGowan.

The court concluded that the delay in the case was substantial and covered a period of significantly changed circumstances in air transportation and that the updating of the record the board did operated significantly to just Pan Am's detriment while it ignored other new information which might have been to its advantage

Pan Am has been seeking approval to operate some domestic routes on the grounds that they would improve the flag carrier's efficiency and strengthen its international services.