The Pirates had won nine of 11 coming into the series with the Rockies, but were outscored 19-7 in the three losses and their lead over St. Louis in the National League Central was reduced to three games.
Colorado overcame an early 2-0 deficit and tied the contest in the sixth with an unearned run.
Wilin Rosario then singled with two out in the seventh and scored from first Arenado's double to right off Bryan Morris (5-5).
That gave the win to reliever Manny Corpas (1-2), who threw a perfect seventh in his lone inning of work.
Pittsburgh put runners on second and third with one out in the ninth, but Rex Brothers escaped the jam to claim his 10th save.
Colorado had not swept a three-game series since April, when they did so against the New York Mets.