Neil Walker, Josh Harrison, Russell Martin and Andrew McCutchen all drove in two runs for Pittsburgh, which avoided being swept in the four-game series.
Volquez has a 0.90 ERA in winning four consecutive starts for the first time in his career. He struck out five and walked two.
Shelby Miller allowed four runs in five innings. He walked four and struck out one.
Walker extended his hitting streak to a season-high 12 games with a two-run double in the fifth that extended the Pirates lead to 4-1. McCutchen started the three-run uprising with a run-scoring single that broke a 1-all tie.
McCutchen drove in a run in the sixth with a sacrifice fly. Harrison added a two-run double in the inning that made it 6-1.