The Reds, who have put themselves in solid contention for a wild card berth with seven weeks remaining in the season, won their third in a row.
Bronson Arroyo (10-9) gave up a run on four hits in seven innings to get the victory and he was backed up by early clutch hitting from Votto.
Votto singled home a run in the first, tripled in another in the third and then scored on a double by Jay Bruce. A double by Chris Heisey brought in Votto with another run while the Reds were scoring twice in the fifth and Phillips contributed his 14th home run of the year in the sixth.
San Diego lost its third straight in the opener of a six-game road trip. Andrew Cashner (8-6) suffered the setback, allowing four runs on seven hits in five innings.