PHILADELPHIA -- Aaron Altherr came through in a clutch spot again.
"Big spot in the game, those kinds of moments I focus in a little more," said Altherr, who had a game-ending RBI single against Pittsburgh on Sunday. "My timing has definitely been better. I feel a lot more relaxed at the plate."
Arrieta (3-0) allowed three runs -- one earned -- and four hits in seven innings. He pitched out of a bases-loaded, no-out jam in the fourth after walking in a run.
"It was a grind," Arrieta said. "I didn't get a consistent feel for my breaking pitches but I kept them off-balance."
The Diamondbacks had won eight straight games in Philadelphia, dating to 2016.
Greinke (2-2) gave up five runs and nine hits in six innings, striking out nine.
"I didn't think I was very good the entire game," Greinke said. "I made a bad pitch on the homer. I wanted it down and he put a really good swing on it."
Carlos Santana hit a double off the top of the right-field fence to start Philadelphia's sixth and Odubel Herrera walked. After Greinke fanned Rhys Hoskins, Altherr hit a 2-1 slider over the bushes behind the wall in straightaway center field to give the Phillies a 5-3 lead.
Arrieta, the 2015 NL Cy Young award winner with the Cubs, has been outstanding in four starts for Philadelphia. The Phillies are off to a 15-8 start.
"Jake is one of the best leaders I've ever been around," Phillies manager Gabe Kapler said. "He models the behavior we want from (everyone)."
Arrieta then walked Chris Owings to force in a run. But Jarrod Dyson hit a bouncer to the mound and Arrieta threw home to get the first out. Franco then made an excellent, backhanded play on Jeff Mathis' sharp grounder, stepped on third and threw to first for a double play.
"We had a golden opportunity," Diamondbacks manager Torey Lovullo said. "Unfortunately, it didn't go the way we wanted it to."
Hernandez led off Philadelphia's first by lining a double to right and advanced to third on Dyson's fielding error. He scored on Santana's groundout.
David Peralta's sacrifice fly tied it at 1 in the third. Herrera's sac fly gave the Phillies a 2-1 lead in the bottom half. Descalso's sac fly put the Diamondbacks up 3-2 in the sixth.
Arrieta has allowed three earned runs or less in each of his last 18 starts, posting a 2.16 ERA in that span.
Arizona's pitching staff struck out 10 or more batters for the third straight game, and the 15th time this season.
Herrera has reached safely in 25 straight games, extending his career-high streak.
Diamondbacks: RHP Taijuan Walker had Tommy John surgery on Wednesday in New York. RHP Shelby Miller, who is recovering from Tommy John surgery performed last year, threw his first session of live batting practice Wednesday. He could return this summer.
Phillies: GM Matt Klentak said RHP Jerad Eickhoff could return to the starting rotation by the end of May. Eickhoff has been out with a strained muscle in his back since spring training.
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