Phillips also had an RBI single in the third and a scored on a double by Jay Bruce, then started a spectacular double play at second base in the sixth to end the inning and halt a Milwaukee threat.
The Reds won for the fifth time in seven games, coming up with five innings of one-run relief pitching.
Cincinnati held a 3-2 lead when Phillips hit his home run in the seventh. That score became essential when closer Aroldis Chapman allowed a run on a wild pitch in the ninth on the way to his eighth save.
It was the opening contest of a 10-game Milwaukee road trip and the Brewers have lost seven out of eight.