Bradley (6-8) allowed six hits and walked two, but by minimizing the damage he was able to allow just two runs over six innings.
"Especially when you see the games we've had here this year, to get out of here with two runs through six I'm really pleased with [that]" Bradley said. "People don't realize how tough that lineup is especially [DJ] LeMahieu, CarGo [Carlos Gonzalez], [Nolan] Arenado, I mean that's some tough guys to pitch to and what this field does so you have to be on top of your game the whole time."
D-backs manager Chip Hale agreed.
"Did a great job," Hale said. "That's a tough lineup to navigate always here in this ballpark. It wasn't pretty, but a lot of times here it isn't. You've just got to keep battling, don't give in and let your guys play."
In the first inning, Bradley allowed a leadoff single to Raimel Tapia and then threw wildly trying to pick him off first. Tapia advanced to third on the error and scored when DJ LeMahieu followed with a single.
Bradley, though, was able to work out of the frame without further damage.
"It was frustrating to give that run away in the first after we scored," Bradley said. "But I felt like I did a good job of settling in after that and really just tried to minimize the damage after that."
In the fourth, Bradley allowed a leadoff triple to Nolan Arenado, but almost was able to pitch around it by striking out the next two hitters.
Daniel Descalso then drew a walk and Tony Wolters singled to center to score Arenado.
Again, though, that was all the Rockies would get as Bradley stranded two runners.
"Worked really hard to [strike] two guys out and then kind of, not gave in, but just got too much of the plate to Wolters and he did a good job hitting it," Bradley said.
Said D-backs catcher Tuffy Gosewisch, "I thought he pitched his butt off after that triple."
Being able to not get frustrated and let things spiral out of control is another sign of maturity for Bradley, a first-round Draft pick (seventh overall) in 2011.
Gosewisch saw that firsthand when he caught Bradley earlier this year in Triple-A Reno.
"In Reno I think he did that and then he came up here and had to do it at a new level and I thought today he did a really good job," Gosewisch said. "My key to every pitch is it doesn't matter what's already happened you've got to focus on this hitter."