Henry Blanco's first home run of the season -- a two-run shot in the top of the sixth -- gave the Diamondbacks a 6-0 lead.
Arizona starter Joe Saunders took that lead and a one-hitter into the bottom of the inning but the Reds opened the sixth with singles from Drew Stubbs and Wilson Valdez before Phillips hit a home run down the left-field line that cut the deficit in half.
Diamondbacks reliever Bryan Shaw (1-4) got an out but then walked two batters. Valdez reached on an error by first baseman Paul Goldschmidt that allowed a run to score.
Phillips then laced a double into the gap in left-center that tied the score and scored the final run on a single from Todd Frazier.
That made a winner of Alfredo Simon (2-1), who pitched 1 2/3 innings of one-hit relief. Closer Aroldis Chapman came on and struck out two in the ninth to get his 15th save.
Goldschmidt singled in a run for Arizona in the first and Aaron Hill singled in another in the third. Hill's home run in the fifth made it 3-0. Chris Young hit an RBI double and Blanco the home run in the sixth for the six-run lead.