U.S. unemployment dropped to a half-century low in September and job growth continued at a modest pace, signs the economy is holding up despite a broader global slowdown.

The jobless rate dropped to 3.5% in September from 3.7% in August, marking the lowest rate since December 1969 when it also logged in at 3.5%. Employers added 136,000 jobs in September, and payrolls for August and July were revised up, the Labor Department reported Friday.

Job...