Mat Latos (5-2) gave division-leading Cincinnati its second straight well-pitched game against the Indians, giving up two runs on seven hits with seven strikeouts over seven innings.
Johnny Cueto threw a complete game for the Reds Tuesday.
Cincinnati was clinging to a 3-2 lead in the seventh when Phillips hit his homer off reliever Nick Hagadone.
Phillips also singled in a run in the first and scored in the fourth on a sacrifice fly by Ryan Ludwick to give the Reds the lead for good.
Aroldis Chapman gave up a solo homer to Jose Lopez in the ninth, but picked up his seventh save.
Derek Lowe (7-5) allowed three runs on five hits and six walks over six innings to take the loss.
Celebrity Families of 2014 [PHOTOS]