Fiers (2-2) notched his second win in his fourth major league start, holding the Twins to four hits while walking two and striking out five.
The right-hander tossed 64 of his 107 pitches for strikes as the Brewers cliched their three-game interleague set at Target Field.
Braun and Aramis Ramirez socked back-to-back solo homers in the third inning and the Brewers outfielder added another bases-empty clout in the fifth, going 3-for-4 overall.
Cody Ransom also went deep for Milwaukee.
Twins starter Liam Hendriks (0-3), recalled from Class AAA Rochester before the game, was touched for five runs (only two earned) on eight hits over five innings.
Ben Revere supplied two hits and an RBI in the Twins' loss.