Cueto (3-0) walked a batter and hit another in the first, but got out of that jam and did not give up a hit until Brandon Inge singled with one out in the fifth. Inge was promptly erased in a double play.
Cueto did not allow another batter to reach base and struck out six while throwing 106 pitches.
Phillips also scored on a wild pitch during a two-run eighth and the Reds benefited from two bases-loaded walks in the ninth.
Wandy Rodriguez (6-3) gave up both home runs in a seven-inning effort to take the loss. He had been trying to extend his personal winning streak to five straight starts.
Pittsburgh had won three in a row and nine out of 11.
Notable deaths of 2014 [PHOTOS]