Fiers (9-7) held the Cardinals to one run on five hits, worked around three walks and struck out five for Milwaukee, which clinched its three-game series.
His run-scoring single in the second inning followed an RBI by Carlos Gomez and staked the Brewers to a 2-0 lead, which they never surrendered.
Milwaukee's bullpen combined to limit St. Louis to two runs over four innings and John Axford picked up his 27th save.
Jake Westbrook (13-11) absorbed the loss, surrendering three runs on seven hits over five complete innings for St. Louis, which saw its lead over the Los Angeles Dodgers for a National League wild card spot shrink to one-half game.
Skip Schumaker, David Descalso and Adron Chambers drove in runs for the Cardinals.
Kate Middleton recycles dress at movie premiere
Gal Gadot cast as Wonder Woman for 'Batman vs. Superman'