The nation's civilian unemployment rate plunged from 10 percent to 9.5 percent last month, its largest one-month decline since 1959, the Labor Department said yesterday.

The seasonally adjusted jobless rate, which peaked at 10.8 percent last December, dropped below the double-digit mark in July for the first time in 10 months and returned unemployment to its June 1982 level.

Unemployment among black workers fell sharply--the "first sign of a reduction in joblessness for this group in many months," said Janet L. Norwood, commissioner of the Bureau of Labor Statistics.

The number of workers with jobs also surged sharply, as employment grew by 500,000 jobs.

The fall in unemployment from 10 percent in June was caused largely by a decrease in unemployment for women, whose jobless rate declined from 8.6 percent to 7.9 percent, the Labor Department said.

The rate for black workers dropped from 20.6 percent to 19.5 percent during July. However, Norwood noted that the gap between white and black unemployment remained large.

The number of people holding jobs increased to a record 101.3 million. Job gains were widespread in manufacturing and construction as well as services, where most of the increases for women occurred.

Employment and unemployment statistics are based on a monthly sample of households. Another measure, based on a survey of nonagricultural businesses, showed an increase in payroll employment of 487,000 to 90.3 million. It was the largest monthly gain this year and the fourth straight strong increase, the government said.

"We know that our economic policies are working, and they are getting Americans back on the job," President Reagan said. "We've turned the situation around and given the American people hope. There's one way we can tell our program is beginning to work. They don't call it Reaganomics any more."

House Speaker Thomas P. (Tip) O'Neill (D-Mass.) said that, although the unemployment decline is "good news . . . we still have a long way to go with 10.6 million Americans out of work. The big question is not the initial strength of the current recovery; it is its duration."

The sharp drop in unemployment and the increase in jobs are the latest indications that the economic recovery is moving briskly, and they suggest that the large spurt in the economy during the second quarter is continuing, economists said yesterday.

"The improvement in unemployment is far greater than almost all previous forecasts," said Martin Feldstein, chairman of the Council of Economic Advisers. "The sharp rise in the July employment level is a clear indication that economic activity in the third quarter has gotten off to a very strong start. The new figures appear to confirm that the rise in GNP this quarter can be in the same range as the second quarter's sharp growth spurt."

Gross national product in the second quarter this year grew at a rapid rate of 8.7 percent a year. Economist Alan Greenspan said the figures released yesterday suggest that third-quarter real GNP would grow at an annual rate of 9 percent if the expansive trend continues in August and September.

"The current recovery has been very strong in comparison to previous ones," said Norwood, the government's keeper of labor statistics. "Overall employment growth eight months after the trough has been sharper both on a numerical and percentage basis than in any of the prior six recoveries," she said.

The seasonally adjusted unemployment rate in the District declined from 10.7 percent to 10.2 percent in June. Unemployment in Maryland dropped from 6.6 percent in May to 6.5 percent in June, and the rate in Virginia declined 0.2 percentage point to 5.8 percent in June.

Nationally, the number of people unemployed for more than six months declined by 365,000 during July to 2.6 million, the first real decline in the long-term jobless group in two years, the Labor Department said. The average rate of unemployment dropped from 22 weeks in June to 21.7 weeks.

While unemployment rates for adults declined, the rate for teen-agers remained unchanged at 23 percent, the Labor Department said.

Last month was the first time that the portion of the black population with jobs reached 50 percent in about 18 months, Norwood said. The proportion of adult black men with jobs was 62 percent compared with 73 percent for adult white men. The unemployment rate for black teen-agers remained largely unchanged at 48.1 percent compared with 19.5 percent for whites aged 16 to 19.

While the decline was "encouraging, it's still a depression for blacks," said a spokesman for the NAACP.

The unemployment rate for all Hispanics was 12.3 percent, down from 14 percent in June.

The number of discouraged workers also declined, but "obviously, anyone who is unemployed still and wants a job has some problem," Norwood said.

Andrew F. Brimmer, a former member of the Federal Reserve Board, said the lag in the improvement in unemployment rates for women and blacks is typical of an economic recovery.

During a recovery, white men are called back to work first, then women and blacks, Brimmer said. Large decreases in women's joblessness is due to a large expansion in the services sector, where large numbers of women are employed, he said.

The average workweek of nonfarm production workers was unchanged from May and June levels at 35.1 hours, the Labor Department said. Manufacturing hours rose 0.1 hour to 40.3 hours a week in July. Seasonally adjusted average weekly earnings rose slightly from $281.34 to $282.85 in July.