The rate was down 0.1 point from August.
Job gains were less than expected and less than the 181,000 average gain of the past eight months but the unemployment rate has not been this low since November 2008.
Also on the positive side, the number of jobs gained in August was revised higher from 169,000 to 193,000, which was offset partly by a 15,000 drop in the July estimate to 89,000.
The BLS report, delayed two weeks by the government shutdown, said non-farm payrolls rose 148,000 in the month, but the number of unemployed was little changed at 11.3 million workers.
"In sum, private sector employment rose by an average of 129,000 per month in the third quarter, lower than we can be fully satisfied with, partially reflecting the effects of fiscal contraction," said Jason Furmon, chairman of the White House Council of Economic Advisers in a statement.
"This underscores the continued importance of taking steps that speed the recovery and boost job creation while avoiding self-inflicted wounds like a government shutdown and debt ceiling brinkmanship that have the opposite effect," he said.
The telling number in the report is 522,000, which is how many fewer workers since June are listed as unemployed, meaning the lower unemployment rate is being influenced not only by jobs added but by the number of persons leaving the workforce.
Those listed as long-term unemployed -- those without jobs for 27 weeks or more -- was little changed at 4.1 million in September, but is down by 725,000 since September 2012, the bureau said. Currently, the number of long-term unemployed comprise 36.9 percent of those unemployed.
"Despite the slowing in the rate of job creation, the September increase means non-farm payrolls have now risen continually for three years," said Chris Williamson, chief economist at research firm Markit Economics.
During the three-year stretch, the unemployment rate has dropped from 9.8 percent to 7.2 percent, Williamson noted.
The bureau said construction added 20,000 jobs in September, while wholesale trades gained 16,000. Transportation and warehousing added 23,000 positions in the month.
Professional and business services jobs also expanded, adding 32,000 jobs in September. Retail added 5,000 jobs and financial jobs declined by 8,000, the bureau said.