It was the third time in five starts that he held an opponent to two runs or fewer while throwing at least 5 2/3 innings, and the outing served as a nice bounce-back from Wednesday's loss when the White Sox scored seven runs off him.
"I thought it was good; he was matching [Greinke] pretty early," Houston manager A.J. Hinch said. "They had a hustle double and another hustle double to get the run across. And then he ran into a little trouble in his last inning. But, all in all, his breaking ball was a little bit better. His slider was back. That was a key pitch that he hadn't had the last start or two."
McHugh surrendered six hits, just one more than Greinke. However, five of those hits went for doubles, and those extra-base hits eventually caught up to him.
The D-backs got on the board in the second when Daniel Descalso laced a two-out double, and Ketel Marte followed with a double to center to make it 1-0.
Arizona ended McHugh's day in the sixth when Jake Lamb smashed a double to left and Paul Goldschmidt followed with another double that pushed across the second run.
"I felt pretty good for the most part," McHugh said. "Got myself into a little bit of trouble in the fifth and sixth with fastball command. I got behind in counts all night tonight. They got deep into counts, and when you get deep in counts like that, sometimes it turns into a 50/50 coin flip. I feel like I made some good pitches, but it's tough. They have a really big outfield. ... So it feels like any ball that gets over the second baseman or shortstop's head has got a chance to be a double."
A handful of Arizona's extra-base hits looked like they might have gone for singles when they initially left the bat, but some heads-up baserunning by the D-backs helped extend singles to doubles.
"Against an offensive team in this ballpark that is pretty aggressive. ... You know, they run the bases about as aggressively as anybody," Hinch said. "It was a challenge for him because he knew he had a small margin for error facing Greinke, but all in all, I thought he pitched well."
Jarrid Denney is a reporter for MLB.com and covered the Astros on Monday.