For the first time in this decade, the U.S. civilian unemployment rate fell below 6 percent last month as the nation's industrial sector continued to strengthen, the Labor Department reported yesterday.

The rate dipped from 6 percent in August to 5.9 percent last month, its lowest level since November 1979, when the rate was also 5.9 percent. There were 112.8 million people at work last month, up from 110 million a year earlier.

In the past 12 months, the unemployment rate has gone down by 1.1 percentage points as moderately strong economic growth led to creation of new jobs faster than workers joined the labor force.

The number of people out of work dropped from 8.3 million a year ago to 7.1 million last month. In addition, in the third quarter about 1 million people were not looking for work because they thought they could not find a job, a number that fell by about 140,000 over the past year, the department said.

"The improvements show that the expansion continues as we enter the 59th straight month of economic growth, a peacetime record," White House spokesman Marlin Fitzwater said.

In September, the Labor Department's monthly survey of households showed that both the size of the labor force and the number of people at work fell slightly. Department officials said the declines may have been the result of distortions arising from seasonal adjustments as many students returned to school.

A survey of industrial payrolls continued to indicate healthy job gains, however. Payrolls grew by about 130,000 jobs last month. Janet Norwood, commissioner of labor statistics, said the increase would have been about 200,000 except for a jump in the number of workers on strike. Strikers are counted in the household survey as being employed, but they are not at work and therefore not counted in the payroll survey.

Manufacturing employment rose by 55,000 last month, with large gains in the steel and machinery industries. Since June, the economy has produced 165,000 factory jobs, raising the manufacturing employment level to its highest point since August 1985.

A recent surge of factory orders, including many from foreign purchasers, has led to both increased production and a rise in the backlog of unfilled orders. At the same time, some previously weak parts of the economy are recovering.

For instance, since the beginning of this year, employment in the oil and gas industry, which dropped sharply along with oil prices last year, has gone up by about 40,000 jobs.

Norwood said the recent industrial recovery has affected the relationship between the jobless rates for men and women. "During the recession of the early 1980s, the predominantly male factory work force was hard hit, and the employment rate for men shot upward, surpassing the rate for women," she told Congress' Joint Economic Committee.

"Partly because of the growth in factory jobs over the last few months, the rate for adult men has fallen to 5 percent in September, while the rate for adult women, at 5.4 percent, has shown little improvement," she said. The rates for men and women had mirrored each other at nearly 6 percent in December and had fallen together to 5.5 percent in April.

"The jobless rate for teen-agers has been relatively sticky," Norwood said. "There has been considerable anecdotal evidence of localized labor shortages and rising wages in some jobs traditionally held by young people. Even so, their unemployment rate, at 16.3 percent in September, has shown less relative improvement than the adult rates."

Nevertheless, the unemployment rate for black teen-agers, who usually have the highest rate of any group in the country, was 29.7 percent last month, down from 38.4 percent in September 1986. With 928,000 black teen-agers in the labor force last month, 276,000 wanted either part-time or full-time jobs but did not have them.

The department also reports seasonally adjusted employment figures for the 11 states in which its survey sample is large enough to give reliable statewide data. The rates for these 11 states ranged from a low of 2.5 percent for Massachusetts to a high of 8.5 percent in Texas. The only other states in the group with unemployment rates above the 5.9 percent national average last month were Michigan at 7.8 percent and Illinois at 6.4 percent.

Another measure of unemployment that counts the 1.7 million members of the armed services stationed in the United States as part of the work force also dropped 0.1 percentage points in September, to 5.8 percent.