Joey Votto also hit a solo shot and scored twice in helping the Reds win their fourth straight.
The Cubs jumped to a 3-0 lead in the second, but Cincinnati rallied with a five-run fourth. Votto delivered the first run of the big inning with his homer and Hanigan's three-run blast put the Reds in front to stay.
Chicago inched within a run in the eighth, but Cincinnati came up with two insurance scores in the bottom half of the inning when Phillips hit his home run to left-center with Votto on base.
Bronson Arroyo (5-4) picked up the victory, giving up three runs on six hits in six innings. Aroldis Chapman put two men on base in the ninth before picking up his 11th save.
Chicago starter Scott Feldman (4-4) hit the first home run of his career, but he also gave up five runs on seven hits over 5 1/3 to take the loss.
The Cubs have dropped five in a row.