Shut down by Brandon McCarthy for the first eight innings, the Phillies scored two runs in the ninth against fill-in Diamondbacks closer Heath Bell.
Jimmy Rollins singled with one out in the 10th off Matt Reynolds (0-1), and Chase Utley followed with his fourth hit, a double to the corner in right.
Hitless with nine strikeouts in his previous 18 at-bats, Howard followed with a floating single to right over Arizona's drawn-in infield.
Justin De Fratus (1-0) got the final out in the ninth inning for his second career victory and Jonathan Papelbon worked a one-hit 10th for his seventh save in as many chances.
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