Leake (8-4) was pulled after allowing a single with one out in the ninth. He also walked four and struck out two. One of the hits he allowed was the first career home run by Sean Halton.
Cincinnati's Shin-Soo Choo nearly matched the Brewers' hit total with three hits of his own. He and Zack Cozart each scored twice, and Jay Bruce added two RBI to Phillips' three.
The Reds scored in five innings with most of the damage inflicted against Milwaukee starter Johnny Hellweg (0-3), who gave up four runs on four hits and five walks in 4 1/3 innings. His replacement, Donovan Hand, allowed a pair of runs on three hits and a walk in two innings.
Choo opened the game with a ground-rule double and, two outs later, Phillips singled him in. The Brewers tied the score in the bottom of the inning with a Carlos Gomez sacrifice fly, set up by two hits -- half of the total against Leake.
Devin Mesoraco drove in a run in the second and Phillips got another run home on a fielder's choice in the third.
The Reds went up 4-1 in the fifth with Bruce driving in Cozart. Halton led off the Milwaukee fifth with his home run.
Phillips again knocked in Choo with a single in the seventh and Bruce followed with another RBI base hit to complete the scoring.