With the score tied 2-2 in the bottom of the ninth, Dolis (2-4) issued a single to Jose Tabata and walked Josh Harrison before retiring the next two batters. He walked Neil Walker to load the bases and then hit Hague with a pitch, pushing Tabata across with the game-winner.
Joel Hanrahan (2-0) got credit for the victory after tossing a scoreless top of the ninth for the Pirates, who clinched their three-game set against the free-falling Cubs.
Pittsburgh starter Kevin Correia allowed two runs on five hits in a 6 1/3-inning stint.
Paul Maholm started for the Cubs, allowing two runs on four hits with five walks and two strikeouts over five innings.
Alfonso Soriano homered for Chicago, which is on its worst losing streak since opening 0-14 in 1997.