After spotting the Rockies an early 5-1 lead, the Pirates took the lead for good with five runs in the third, highlighted by Jones' blast.
James McDonald (10-3) turned in his sixth straight start without a loss despite getting tagged for six runs on nine hits over five frames.
Brad Lincoln, Jason Grilli and Tony Watson teamed up on three innings of shutout relief and Joel Hanrahan picked up his 26th save for Pittsburgh, which entered the contest a game behind National League Central-leading Cincinnati.
Rockies reliever Matt Reynolds (3-1) absorbed the loss.
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