PHOENIX -- Jake Lamb and Zack Greinke accomplished some firsts Tuesday, when they combined to help Arizona to its first home series victory of the season.

Lamb homered for the second straight night, a career first, and Greinke permitted a season-low five hits in seven-plus innings in the Diamondbacks' 5-3 victory over the New York Yankees on Tuesday at Chase Field.

Lamb's two-run homer off right-hander Michael Pineda (1-5) gave the Diamondbacks a 5-1 lead in the fifth inning. Lamb had a three-run homer in the fifth inning of a 12-2 victory Monday.

"Definitely caught me off-balance the first two 'ABs,' " Lamb said. "I just tried to shorten up a little bit. Threw a pitch in and I got barrel to it.

"All the great players can make adjustments between at-bats. I'm trying to minimize time, whether it is a couple of days bringing it down to a day, then a few ABs. It is something you are always working on."

Greinke (4-3) pitched into the eighth inning for the first time this season, leaving after Didi Gregorius and Aaron Hicks singled.

Right-hander Daniel Hudson entered and gave up a run-scoring groundout and an RBI single to Jacoby Ellsbury to make it 5-3 before striking out Brett Gardner and Mark Teixeira to end the inning. Hudson pumped his fists and shouted as he left the mound.

"I don't know if he is always that fiery," Greinke said. "That was pretty intense."

Paul Goldschmidt and Nick Ahmed had two hits and an RBI as the Diamondbacks (19-23) won their second straight to secure their first home victory in seven series. They are 7-16 at home.

Brad Ziegler pitched around a two-out walk in the ninth inning for his eighth save.

Starlin Castro had two of the five hits off Greinke, his fifth homer of the season in the second inning and a single in the seventh.

Greinke recorded his fourth victory in his last five decisions, giving up Starlin Castro's homer in the second before the Yankees scored again in the eighth. Greinke struck out seven and did not walk a batter, dropping his ERA to a season-low 5.08.

"That's Zack," Lamb said. "He's one of the best. He was throwing some nasty pitches, and he was locating like he always does. He was biting on the corners, and they were chasing that changeup and that slider."

Greinke did not pitch out of the stretch until after Dustin Ackley's pinch single with one out in the sixth inning.

"That was nice," Greinke said. "I'm not quite as good from the stretch, I feel like. So made it a more comfortable game."

Greinke would not call it is his best outing, pairing it with his 2-1 victory in San Francisco on April 20, when he gave up one run and six hits in 6 1/3 innings.

Pineda gave up five runs and nine hits in five innings, raising his ERA to 6.60. He walked one and struck out nine. His ERA is the highest among the 52 qualifiers in the American League.

"The big blow was when he pulled a fastball in the fifth inning and it was a two-run homer," Yankees manager Joe Girardi said of Pineda. "He was trying to go down and away and it ended up inside, thigh high.

"There is just some inconsistency in his slider. We will get it worked out. We have to get it worked out. He is better than what he has performed and we will get it straightened out."

Castro's homer with one out in the second inning, measured at 420 feet, gave the Yankees a 1-0 lead.

The Diamondbacks tied it in the last of the second on a two-out triple by Chris Owings and a single by Ahmed. Owings has hit safely in eight of his last nine games.

NOTES: The Yankees promoted INF/OF Rob Refsnyder, RHP Luis Cessa and LHP James Pazos on Tuesday, optioning RHP Chad Green and RHP Conor Mullee and designating LHP Phil Coke for assignment. Green and Mullee made their major league debuts in a 12-2 loss to Arizona on Monday, with Green giving up six runs (four earned) in six innings to take the loss. Refsnyder could be used at second base, third base and right field, Yankees manager Joe Girardi said, although INF Ronald Torreyes is likely to remain as the backup at third base. ... Arizona RHP Rubby De La Rosa will be skipped the next time through the rotation, manager Chip Hale said, because of off days Thursday and next Monday. De La Rosa, whose 3.53 ERA is the lowest among Arizona starters, has been dealing with nagging groin and blister issues, Hale said. ... Yankees RF Carlos Beltran received a start off Tuesday, although he pinch hit in the eighth inning. He has played in all 38 games this season, starting 35. ... Yankees DH Alex Rodriguez is expected to come off the disabled list Thursday when eligible. "I'm not sure what his day is yet," manager Joe Girardi said. "There are some hoops he has to jump through when it comes to running, to make sure he passes all the tests before we activate him."