Bruce and Phillips each stroked two-run doubles in the seventh inning when the Reds broke open a close game by scoring four runs, increasing their lead to 8-2.
Ramon Hernandez homered among two hits and Scott Rolen added a pair of hits and an RBI for the Reds, who wrapped up their first three-game sweep over St. Louis since 2006 and improved their National League Central lead to 1 1/2 games over the Cards.
Travis Wood (3-3) earned the victory, yielding only back-to-back solo homers to Lance Berkman and Yadier Molina in the second among seven hits.
But the Reds' bullpen had to hang on as the Cards scored five runs in the ninth, highlighted by a two-run double by Ryan Theriot and Allen Craig's steal of home.
Chris Carpenter (1-3) was rocked for eight runs (seven earned) on nine hits over 6 1/3 innings, walking two and fanning five for St. Louis.