Drew's shot into the pool area beyond the right-center field wall at Chase Field put the Diamondbacks up 6-2 and ultimately snapping a two-game losing streak.
Randy Johnson (2-1) got the win despite giving up four runs on five hits over six innings. He struck out six. Relievers Chad Qualls, Tony Pena and Brandon Lyon each pitched a scoreless inning. It was Lyon's 10th save.
The Phillies' runs came mostly from Eric Bruntlett, who homered, doubled and knocked in three runs. Jayson Werth hit a solo homer for Philadelphia, which lost for the fourth time in its last 12 games.
Adam Eaton (0-1) was the loser after giving up six runs on five hits in four innings. He was tagged with no-decisions in his first six starts.