The benefits of a strong job market are spreading in the form of higher wages for many of those left behind for much of the past decade’s economic expansion, including young Americans, low-income households and people with the least education.

The unemployment rate in September fell to 3.7%, its lowest level since 1969. That is creating worker shortages and wage gains, not just for high-skilled workers who tend to command the best pay but also for low-skilled and blue-collar workers whose wages lag behind.

A...