Wages for rank-and-file workers are rising at the quickest pace in more than a decade, even faster than for bosses, a sign that the labor market has tightened sufficiently to convey bigger increases to lower-paid employees.

Gains for those workers have accelerated much of this year, a time when the unemployment rate fell to a half-century low. A short supply of workers, increased poaching and minimum-wage increases have helped those nearer to the bottom of the pay scale.

Pay...