The Pirates came up with three solo homers in the sixth to cut into a five-run deficit, but five Cincinnati relievers combined to shut down Pittsburgh over the last 3 1/3 innings.
Chris Heisey put the Reds in front with a first-inning, solo homer and the Reds then batted around in the fifth.
With runners on first and third, Heisey's infield single brought home pitcher Mike Leake with the first run of the frame. Joey Votto drew a walk that loaded the bases and Phillips came through with his double to deep center.
Aroldis Chapman gave up a two-out single in the ninth on the way to his 22nd save.
The loss went to Francisco Liriano (9-4), who allowed five runs on five hits in 4 1/3.