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.
Gal Gadot cast as Wonder Woman for 'Batman vs. Superman'
Toddler uninjured after being knocked over by Obama family dog