PHOENIX -- When the ball left Tyrone Taylor's bat, D-backs ace Zac Gallen thought for sure his scoreless streak had ended. With Luis Urías running from first base with two outs and the ball headed toward the deepest part of Chase Field in right-center, there seemed to be little doubt that if the ball fell, the Brewers would score a run.

But Arizona right fielder Daulton Varsho had other plans. He covered 104 feet in time to haul in the ball at the warning track for the third out of the second inning -- a 5-star grab with a catch probability of 5 percent, per Statcast.

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"Varsho made an unbelievable play," Gallen said. "Honestly, I was like, 'Oh man, there it goes, unless it bounces over the fence for a ground-rule double.' But Varsh is unbelievable out there. If he's not the best right fielder defensively in baseball, he's definitely up there. So yeah, he made a great play."

Outside of a fly ball to the warning track by Hunter Renfroe in the seventh, that was as close as Milwaukee came to scoring against Gallen, who tossed seven dominant innings to run his scoreless streak to 41 1/3 innings, leading Arizona to a 5-1 win and a series victory.

Gallen's streak is the eighth longest in the Live Ball Era (since 1920). He is the fourth AL/NL pitcher in the Modern Era (since 1900) to throw six or more scoreless innings in six straight starts, joining Don Drysdale (1968), Orel Hershiser (1988) and Zack Greinke (2015).

The D-backs’ record for consecutive scoreless innings is owned by right-hander Brandon Webb, who tossed 42 straight in 2007. The Major League record of 59 belongs to Hershiser, who accomplished the feat in 1988.

Gallen has admitted at times during the streak that he's thought about it, going as far as saying that during his Aug. 24 start in Kansas City, he thought too much about it. Since then, he said it's been easier to just focus on getting outs.

"This was another day for Zac," manager Torey Lovullo said. "He goes out there and executes at a very high level and throws up seven more zeros. He spoils us, but it's because he's working his butt off, because he's executing. It's because of the four days in between starts that he is studying, working to make good things happen. It's not by accident that he's on this tremendous run."

For the second straight start, Gallen said he didn't feel like he was in a groove during the first three innings, even though he only gave up one hit -- a first-inning single by Rowdy Tellez -- over that span.

By the fourth, though, Gallen felt comfortable and mixed in all his pitches after primarily leaning on his fastball early. Milwaukee had only one baserunner after the third against Gallen -- courtesy of a fourth-inning single by Renfroe.

“He got in a rhythm, and we were pretty quiet after that," Brewers manager Craig Counsell said. "His curveball is a really good pitch. His changeup is really good to the lefties. We weren’t able to get much going.”

The D-backs will insert rookie Ryne Nelson into their rotation Monday and plan to go with six starters for at least a couple of weeks. With the addition of Nelson -- along with Arizona's off-day on Thursday -- Gallen's next outing is likely to come next Sunday against the Rockies at Coors Field.

"Well, at this point now, I'm right there, so I might as well try and see what the deal is," Gallen said of chasing Webb's franchise record. "I mean, I think I'm only an inning away, so I might as well just try. My job is to go out there and throw up zeros, so it kind of falls into the line of doing my job."

Lovullo said there was no thought of having Gallen go out for the eighth inning for a chance to break the record on Sunday. With the right-hander at 103 pitches, Lovullo did not want to push Gallen any further, a decision that Gallen said he agreed with.