With the game tied 1-1 in the eighth, Drew Stubbs led off with a single and went to second on a wild pitch by Jonny Venters (2-2). One out later Phillips belted a pitch off the top of the left-field wall, easily scoring the go-ahead run.
Heisey later laced a pitch into the left-center field gap for an insurance tally, and the Reds went on to snap the Braves' three-game winning streak.
Lyle Ondrusek (3-0) earned the win in relief of Homer Bailey, who had limited Atlanta to one run on six hit over 6 2/3 innings.
Sean Marshall picked up his sixth save with two strikeouts in the ninth.
Braves starter Randall Delgado pitched well in a no-decision, surrendering one run on four hits over 6 2/3 frames.
Martin Prado went 2-for-4 with an RBI in the loss.