The Phillies had forged a 2-2 deadlock in the top of the eighth on a pinch-hit, two-run homer by Chase Utley.
But Cincinnati responded quickly against the Phillies' Jeremy Horst (0-1).
A pinch-hitting Derrick Robinson singled to lead off the frame, went to second on Shin-Soo Choo's sacrifice and to third when Zack Cozart's fly to right fell in for a double.
That brought up Phillips, who spanked a 1-2 pitch from reliever Mike Adams past diving second baseman Freddy Galvis into right field for a two-run knock.
Aroldis Chapman closed it out with his third save.
Bronson Arroyo (2-1) earned the win after yielding two runs on five hits over eight innings. The right-hander didn't issue a walk and struck out three.
Phillies starter Cliff Lee likewise allowed two runs on five hits over seven full frames.
Celebrity Families of 2014 [PHOTOS]