Bradley pitched a career-best 7 1/3 innings, allowing three runs on four hits and becoming the first D-backs rookie to notch nine strikeouts since Tyler Skaggs in 2013.
"I've taken my two starts previously up here and tried to take the positives and the negatives, go down to Triple-A and continue to fine-tune my craft, continue to work on the things that I felt like I needed to do to stay here permanently," Bradley said. "That's the ultimate goal, is to stay here and never go back down."
Bradley made two spot starts earlier in the season. He allowed five runs in 4 1/3 innings against the Giants on April 18 and picked up a win over the Rockies on May 9 when he allowed four runs in six innings.
But this time, Bradley looked more like the pitcher who has dominated for Triple-A Reno this year, where he is 5-1 with a 1.99 ERA in seven starts.
"In Spring Training, he was pretty sporadic, he didn't really have a feel for his locations," D-backs catcher Chris Herrmann said. "From what I saw today, it looks like he's been putting in a lot of hard work down in Triple-A, and from what he did today, it looks like he belongs here."
Bradley threw 70 of his 97 pitches for strikes and consistently worked ahead in the count, issuing just one walk to the last batter he faced in the eighth. Beginning with one out in the third, he retired 15 of the next 16 batters -- the lone exception was Alexei Ramirez's home run to lead off the fifth.
The former first-round pick could be a nice boost to the rotation for the D-backs, who won just their second home series by taking two out of three from San Diego.
"The maturity level was so high just from conversations we had with him, the conversations we had with him both times sending him out, just the focus he had on getting back and how he was going to get back -- not by luck, but by pitching his way back up here," D-backs manager Chip Hale said. "Now he's done a nice job in his first outing and he's going to continue in this rotation for a while."
Jake Rill is a reporter for MLB.com based in Phoenix. This story was not subject to the approval of Major League Baseball or its clubs.