Calhoun connected on Greinke's fastball in the fourth inning for an upper-deck shot to right. The three-run homer put Arizona ahead 3-2.
His second drive narrowly sneaked by the glove of leaping right fielder Josh Reddick. The solo shot off Blake Taylor in the eight made it 6-3. Calhoun has 14 homers following his second multihomer effort this week.
"I'm feeling really good," Calhoun said. "I can't really explain it. Just the waves of baseball, man. I'm on a high right now, and it's been a lot of fun playing."
Greinke matched his season high with nine strikeouts and pitched three-run ball over five innings. It was his first start against Arizona after being traded to Houston at the deadline last season.
Arizona starter Zac Gallen (2-2) allowed a run in the first inning on a wild pitch and a run in the third inning on a double by Kyle Tucker. George Springer led off the fifth with a homer off the train tracks above left-center field. His 11th home run of the season tied it at 3.
Gallen allowed six hits in six innings, striking out six.
Jose Altuve had his first extra-base hit since Aug. 22, a span of 42 at-bats, with a double into the right-center field gap in the seventh inning. Altuve entered Friday hitting .216.
The Astros have lost 11 of their last 15 and fell to 25-26.
"You've got to go with the guys that have been there, you've got to go with the guys that have got you here," Astros manager Dusty Baker said. "It's a daily game. Tomorrow could be totally different. You've got to go with your core guys -- you have to."
The Astros and Diamondbacks had a pregame moment of silence for Johan Maya, a longtime minor league coach and scout for both organizations. Maya, who spent 15 years with the Astros before joining the Diamondbacks in 2019, died at age 40 of COVID-19 in July.
Calhoun's first homer was estimated just 382 feet, and he wasn't too concerned that that estimate might have been on the short side.
"As long as it went over the yellow line, I don't really care," he said.
HE SAID IT
"He's interesting to watch, that's for sure. He does it really differently and that's pretty cool. He marches to the beat of his own drum, and he's been doing it for a long time so he's obviously got something figured out." -- Gallen on Greinke
Diamondbacks: IF Ketel Marte (wrist) will take batting practice on Saturday with hopes that he could return next week, manager Torey Lovullo said. ... IF Andy Young had a right hamate (hand) bone surgically removed and is out for the season. Young was hit by a pitch at the team's alternate training site. He is expected to be ready for 2021 spring training. Young had five hits in 26 at-bats in 12 games of his first season in the majors.
Astros: RHP Justin Verlander (forearm) is scheduled to throw a simulated game on Monday. Verlander threw 75 pitches in a simulated game on Wednesday at Minute Maid Park. ... RHP Brad Peacock was placed on the 10-day injured list with right shoulder soreness, backdated to Sept. 15. ... Taylor was activated from the 10-day IL.
Diamondbacks: RHP Luke Weaver (1-7, 6.70) will start Saturday, trying to snap his five-game losing streak.
Astros: RHP Cristian Javier (4-2, 3.22) allowed one run on four hits in six innings in an 8-2 win over Arizona on Aug. 4.
More AP MLB: https://apnews.com/MLB and https://twitter.com/AP-Sports
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