Volstad (11-9) gave up six hits without a walk while striking out two for the Marlins, who had dropped the first two games of the series. Osvaldo Martinez had two hits with an RBI and a run scored in the win.
Chris Narveson (11-9) gave up two runs on six hits with a walk and five strikeouts over 6 2/3 innings for the Brewers, who had a three-game winning streak stopped.
Florida got on the board in the first when Cameron Maybin led off with a single, stole second and scored on a Logan Morrison single for a 1-0 lead.
Volstad did not let a batter reach second base through the first five innings and only allowed two baserunners through that time.
The sixth inning saw Volstad give up a one-out single to Narveson, but he retired the next two batters. Mike Stanton led off the seventh with a shot over the wall in left for a 2-0 lead.
Singles from Prince Fielder, Lorenzo Cain and pinch-hitter Craig Counsell in the seventh chased Volstad from the game. Jose Veras came on and got George Kottaras to line out and end the frame.
An RBI single from Gaby Sanchez in the eighth gave Florida a 3-0 advantage, and Leo Nunez struck out the side in the bottom of the frame.
Scott Cousins tripled as a pinch-hitter to lead off the ninth and scored on a Martinez double for a 4-0 lead.
Clay Hensley survived a pair of hits in the ninth to lock down the win.
Florida has now taken four of the seven games against Milwaukee this season...Volstad has won five straight decisions and is 7-1 in his last 12 starts...Cain finished 2-for-4 and was the only Brewer with more than one hit.