"I'm like a little kid in the dugout," Fiers said with a grin. "I want to watch every at-bat he has.
"It could be a ball, and he'll hit it out. It's crazy to see him out there ... it's stupid."
The club previously hit four home runs on April 24 and June 8 against Houston and San Diego, respectively, but both occasions occurred at Miller Park. They last tallied four home runs in a road game on Sept. 16, 2011, in Cincinnati.
Braun's homers boosted his season total to 19 and his Interleague hitting streak to 21 games, during which he's hit six home runs. He went 3-for-4 on the day, walking and hitting a double in addition to his homers.
"He's just got tremendous power," manager Ron Roenicke said. "There's really no ballparks that can hold him in when he hits the ball well."
Aramis Ramirez and Cody Ransom also registered solo home runs, Ramirez's coming directly after Braun's first clout in the third.
Fiers earned his second win, and first since his debut on May 29 against the Dodgers. The 27-year-old rookie limited Minnesota to a single run on four hits over seven innings.
"Their young man threw the ball really well," Twins manager Ron Gardenhire said. "He changed speeds. He moved the ball around. He was locating his fastball and not giving us anything."
Braun's second dinger and fourth in three days came in the fifth inning, just one pitch after Jamey Carroll dropped his popup in foul territory for an error.
The ball sailed an estimated 419 feet, landing in Target Field's right-field flower box.
"I got all of that ball and it barely got out," Braun said. "Most ballparks, it's probably a no-doubter. You have to hit it up high. You're not going to get many cheap homers here."
The reigning National League Most Valuable Player went deep earlier in the third after a lengthy battle with Minnesota starter Liam Hendriks. Braun worked a full count before taking the ninth pitch of the at-bat over the left-field fence.
"He's swinging the bat as good as I've seen it," Hendriks said. "I threw him a 3-2 fastball that was a little bit up and over the plate and he hit it pretty hard. I threw a slider that I didn't get off the plate enough. I was trying to get it over for a ball, but I left it over and he took a swing on that one as well."
Ramirez followed by hitting Hendriks' very next pitch deep for his seventh homer of the season. The back-to-back homers marked the team's first since Alex Gonzalez and George Kottaras accomplished the feat on April 13 in Atlanta.
Ransom homered on reliever Anthony Swarzak's first pitch to lead off the sixth.
Fiers retired six of Minnesota's first seven batters before allowing a run in the bottom of the third. Darin Mastroianni lined a double to the left-field corner, then scored on a two-out single from Ben Revere, trimming Milwaukee's lead to 4-1.
The Brewers manufactured their first two runs in the second. Rickie Weeks led off with a single before Taylor Green reached on another Carroll error, with Weeks taking third. Hendriks retired Ransom via strikeout and Martin Maldonado on a failed sacrifice. But Norichika Aoki belted a single to right, scoring Weeks and Green to give Milwaukee a 2-0 lead.
"You have to add on," Braun said. "We got a couple runs early, but the challenge is to continue to add on. You know you're facing a good team. They're swinging the bats well. They're playing good baseball. So you have to continue to add on."