The Fairfax County Board of Supervisors agreed to redraw the boundaries of their election districts in a way to protect themselves and then toasted each other with champagne at a secret meeting that appeared to violate Virginia's open-meeting law.

The unannounced session, held Friday in the Annandale office of Supervisor Audrey Moore, capped 11 months of jockeying among the county's nine supervisors, each anxious to protect his political base and his job.

Last night the supervisors unanimously endorsed in public session the plan they drew in private on Friday. "It's an incumbents' plan, sure," Supervisor Thomas M. Davis III said after the brief discussion and vote. "What did you expect?"

While producing some peculiarly shaped districts, the supervisors made sure no incumbents will have to run against each other. Liberal Democrat James M. Scott, who had been viewed as the likeliest victim of the redistricting process, had to pick up heavily Republican Oakton, but managed to lose his Republican Cardinal precinct to his Republican neighbor Davis.

Most supervisors refused yesterday to discuss the Friday meeting publicly or even to acknowledge that it took place. "I don't have any comment on any meetings," said Board Chairman John F. Herrity.

Edmund L. Castillo, the county public information director who normally publishes the board's meeting schedule, said he had not been notified the supervisors would meet. Virginia's Freedom of Information Act requires that all meetings of three or more supervisors be publicized and open.

"We just felt that we had to talk it over," said Supervisor Joseph Alexander. "It's been done before, it'll be done again."

Until the Friday session, the supervisors had been meeting two or three at a time in closed-door sessions and trading precincts over the telephone, attempting to find a resolution to the redistricting.

The remapping, which must be sent to the Justice Department by Jan. 1, is necessary because the 1980 Census revealed substantial imbalances in population among the county's eight districts. Justice is required to approve any changes in Virginia's election districts under the 1965 Voting Rights Act.

Since the last redistricting in 1975, the more urban eastern half of Fairfax lost people or held its ground while the once-rural western portion of the county experienced one of the most rapid growth rates in the Washington area.

Democrats now control the board by a 5-to-4 margin, but the reapportionment should give increased power to the younger, often Republican families in the county's newest subdivisions. Neighborhoods in Springfield, McLean and elsewhere have lobbied with success to make sure the shift did not also split their communities.

To all the supervisors except Herrity, who is elected at large, the redistricting had a more personal significance. They drew and redrew maps to make sure their houses stayed in their districts and their districts stayed as friendly as possible.

"Everyone's been edgy for months," said one supervisor. "I think the board has gotten more frantic over this than they really should be," said another.

Both Democrats Scott and Alexander represent older, eastern districts that need more voters to reach the ideal size, and both appeared doomed to expand west into Republican territory. On Friday, however, they found a compromise that should help them in the next board election in 1983.

Alexander, who represents the Lee District, will still have to take some Republican precincts west of Shirley Highway, but he will also move into more friendly territory west of Alexandria and keep most of the Democratic area along U.S. Rte. 1 that fellow Democrat Sandra L. Duckworth had coveted for her Mount Vernon District.

Instead of taking the heavily Republican precincts of Oakton and Vale, as suggested by county staff, Scott's Providence District will get Oakton and the somewhat more Democratic Greenbriar subdivisions. While giving Providence a peculiar elongation, the switch solved several problems.

It allowed Republican Marie Travesky, whose oversized Springfield District had to cede several precincts, to give up voters in the west, where rapid growth and proposed highways have thrown up some sticky political problems, rather than in her home base in eastern Springfield. And that, in turn, allowed Alexander to keep out of Travesky's heavily Republican precincts along Rolling Road.

Republican Davis, meanwhile, agreed to leave Scott with some Democratic precincts along Rte. 50 while taking more Republican subdivisions in Camelot and Price precincts.

That move, however, threatened to redistrict Scott's school board appointee, chairwoman Ann Kahn, right out of Scott's district. So the board cut Price in two, giving Davis as many Republican homes as it logically could while keeping Kahn's house in Providence.

Supervisors Moore, Martha V. Pennino and Nancy Falck, two Democrats and a Republican, appeared to suffer little political damage from the changes to their districts.