Braun finished with three RBIs, shortstop Cody Ransom matched his career high with four RBIs and four Brewers scored two runs apiece to back Fiers, the 27-year-old who overcame a long first inning to deliver the 11th double-digit strikeout game by a rookie in Brewers history.
Fiers was sitting only a few feet away when Braun lauded his contributions to the injury-battered Brewers -- he is 3-2 with a 2.29 ERA in six starts and one relief appearance, has allowed only one run with 22 strikeouts in his last three starts and has not allowed a run over his last 18 1/3 innings.
The admiration, Fiers said, is mutual.
"He's amazing," Fiers said. "[Braun is] a guy that takes a lot of pitches, works the count and also gets hits as well. That's just killing to the pitcher."
Braun, who will get word Sunday morning whether he was voted an All-Star starter for the fifth straight season, took Arizona left-hander Wade Miley deep with the bases empty in the third inning and with a man on in the fourth for his 15th career multi-homer game.
Both home runs came with Braun behind in the count, 1-and-2, the first on a quality fastball low in the strike zone. The second came amid a six-run Brewers fourth inning, highlighted by Ransom's three-run home run.
With his 21st and 22nd home runs, Braun reclaimed the top spot on the NL leaderboard. He had been tied with the Cardinals' Carlos Beltran.
So much for Prince Fielder's departure leading to a dip in Braun's production. Through 72 games, he is batting .313 (versus .311 at the same point last year), with 22 home runs (15 last year), 55 RBIs (51) and a .611 slugging percentage (.562).
"It's not surprising me," Brewers manager Ron Roenicke said. "I always bring it up with last year with Prince and [five-hole hitter Casey McGehee] having an off year. There wasn't any difference in how they pitched to Prince."
Carlos Gomez tripled and homered for the Brewers.
The series, a rematch of last year's National League Division Series, will come down to Sunday's afternoon finale.
Fiers set a career high with 10 strikeouts, becoming the first Brewers rookie to reach double digits since Chris Narveson struck out 10 Cubs in September 2009. Before that, no Brewers rookie had struck out 10 batters since Steve Woodard in 1998.
It was difficult to imagine Fiers getting through six scoreless innings -- he did, allowing only two singles in the second inning and three walks -- during a protracted first. Fiers needed 31 pitches to get through a first inning in which he walked two batters and saw the D-backs fight off eight foul balls.
No Arizona hitter put a ball in play until Fiers' 31st pitch, which induced a Paul Goldschmidt fly out to finally end the inning.
"I wasn't trying to do it that way," Fiers said. "I don't think I want to make a career out of that."
Roenicke credited Arizona hitters for all of those foul balls, but Fiers said the long first inning was on him.
"It wasn't really them, it was me not hitting my spots," Fiers said. "Early on, I was trying to get in a groove and I couldn't."
Fiers needed 17 more pitches in the second inning and 22 in the third, putting him at 70 through three innings. He threw only 35 more pitches over his final three innings, logging half of his 10 strikeouts in that efficient span.
After Brewers reliever Manny Parra struck out three in his lone inning, Tim Dillard gave up two runs, including Miguel Montero's solo shot, over the final two frames.
"It wasn't our night," D-backs manager Kirk Gibson said. "We had our opportunities in the first three innings and the guy [Fiers] was crafty. He wiggled his way out of it and they took control of the game.
"You have to give the guy some credit, we hadn't seen him before. He had lots of trouble and he made some pitches to get out of it."
Fiers will start again Thursday against the Marlins, his final outing before the All-Star break. If the Brewers have right-hander Shaun Marcum (elbow) back from the disabled list to begin the second half, then club officials, unless they want to employ a six-man rotation, or bump Marco Estrada to the bullpen, something Roencike does not want to do, may face a challenging decision.
"I've always thought I could pitch at this level, and this good," Fiers said. "I think I should actually be better this year, but I had a couple of rough ones early on. I'm fine, I'm going to keep working hard and try to do the same the next start."