WASHINGTON—Americans traditionally left behind as jobs and wages grow—high-school dropouts, blacks and Latinos—are reaping the benefits of a tightening labor market, with an unemployment rate that hasn’t been lower in nearly half a century.

The jobless rate in May ticked down to a seasonally adjusted 3.8%, the lowest since April 2000, the Labor Department said. The last time the rate was lower was in 1969.

At the same time, U.S. employers added 223,000 jobs last month, extending the longest continuous job expansion on record to 92 months. Average hourly earnings edged up 2.7% from a year earlier—and raises were even stronger for rank-and-file than managers.

“It’s pretty hard to argue that the labor market is anything but right in the sweet spot,” said Dan North, chief economist at business insurer Euler Hermes North America. “There is tremendous demand for labor right now.”

And those gains are extending to all corners of the labor market. The unemployment rate for women, at 3.6% last month, was the lowest since 1953, when a far smaller share of women sought jobs. The jobless rate for workers older than 24 without a high-school diploma fell in May to 5.4%—near a record low. The jobless rates for blacks and Latinos are also near record lows.