In his last four starts, the left-hander has allowed just four runs over 30 2/3 innings. Sunday's outing lowered his ERA to 2.19, good enough for fourth-best in the National League. But with Ryan Dempster and Brandon Beachy on the disabled list, the only active NL pitcher with a lower ERA is R.A. Dickey.
"He doesn't back down from anybody, he just throws strike one every time," D-backs catcher Miguel Montero said. "He competes and believes in his stuff."
The only blemish against Miley came in the seventh inning, when Alfonso Soriano connected for a solo homer into the first row of the left-center-field bleachers.
"It came out of his hand a little better than it did in the video, especially when things got tough," Cubs manager Dale Sveum said. "That's a pretty good pitcher on the mound when things got tough there. He made pitches that he had to make."
The Cubs put runners on second and third with no outs in the eighth, but the southpaw wiggled out of the jam, retiring the next three batters to end his afternoon throwing a career-high 116 pitches.
"I just wanted to keep the lead, do whatever I could and bear down," Miley said. "Just trusting the game plan, sticking with it and making adjustments late to make pitches."
Miley, who began the season as the D-backs' long-relief pitcher, saved his worn-out bullpen from further wear and tear with his long outing. In the club's previous two games, the bullpen had pitched 14 2/3 innings.
"We had four guys that were shut down in the bullpen today, we needed a performance like that," D-backs manager Kirk Gibson said. "It was his game. He earned that right a long time ago."
With Sunday's victory in hand, Miley now leads the D-backs in wins, ERA and WHIP.
The sweep also left Arizona 10-2 in their last two homestands and with five runs on Sunday, the offense produced 51 total runs against the Mariners and Cubs this week.
"We were clicking on all cylinders, it's always nice to see that," D-backs outfielder Justin Upton said. "We're very capable of scoring runs. You can't expect it every night, but when we get the bats going, we can put up runs."
Jason Kubel continued his stellar month at the plate with another home run, bringing his June total to six, to go with 23 RBIs for the month.
"He's been great protection for me," said Upton, who collected two hits and drove in three. "I hope to see him keep swinging the bat the way he is and getting me good pitches to hit."
Both clubs combined for just two hits in the first five innings, but only the D-backs made the most of theirs. After Gerardo Parra moved to second base on a groundout after a lead-off walk in the first inning, Upton delivered a RBI single to left field to put the D-backs ahead, 1-0.
Five hitless innings later, the D-backs added to their lead in the sixth, when Parra tripled with two outs and Aaron Hill drove him in with an infield single to go up, 2-0.
After Soriano's long ball closed the gap to one, Kubel gave Miley back some breathing room with a solo shot of his own. Upton added a two-run single in the eighth to give Arizona some insurance runs.
"I'm just seeing balls right now," Upton said. "Getting good pitches to hit and getting the barrel on it."