Volquez (2-4) allowed just one run on three hits and two walks while fanning four to secure his first win in six starts.
Andrew McCutchen drove in two runs and Josh Harrison added an RBI for the Pirates, who have won three of their last four games.
In his second major league start, Blake Treinen (0-2) surrendered two runs on four hits and five walks over 5 2/3 innings to absorb the loss.
Ian Desmond's solo home run was one of just five hits for the Nationals, who have lost four of their last six contests.
Swim Week Miami Beach 2014 [PHOTOS]