Phillips put Cincinnati in front with an RBI single in the first inning and made it 5-0 with a bases-loader homer in the third.
The Reds second baseman later drove in another run on an eighth-inning groundout, recording his fourth career six-RBI game and first since 2009.
Homer Bailey (4-4) surrendered just one unearned run on four hits over eight dominating innings, walking two and striking out eight as Cincinnati took the opener of a four-game series.
Cubs starter Scott Feldman (5-5) was tagged for five runs on seven hits over six full frames.
Starlin Castro provided Chicago's only RBI.