Werth's solo shot to deep center off Juan Gutierrez (0-2) proved to be the game-winner, seven innings after his first bases-empty blast had put the Phillies up 1-0.
Raul Ibanez also connected a solo homer for the Phillies, who broke a streak of 45 innings without a round-tripper and won for the third time in four games, raising their April record to 11-6.
Jose Contreras (1-1) got credit for the win after pitching a scoreless eighth while Ryan Madson notched his fourth save of the year despite allowing a one-out single.
Arizona was led by Kelly Johnson, who hit a two-run homer.
Diamondbacks starter Ian Kennedy pitched well in defeat, yielding two runs on four hits with four strikeouts, earning a no-decision.
Celebrity Families of 2014 [PHOTOS]