Losing pitcher Rich Hill had tossed 19 consecutive scoreless innings until Fielder went deep in the fourth. Kevin Mench added a solo homer and Rickie Weeks delivered an R-B-I single in the Brewers' fourth consecutive win.
Suppan is 3-and-2 after holding the Cubs to eight hits over eight shutout innings. Francisco Cordero struck out Cliff Floyd for his eighth save after Derrick Turnbow gave up Mark De Rosa's R-B-I double in the ninth.
Hill was reached for four runs and six hits in six and two-thirds, dropping him to 3-and-1.
The Cubs have dropped three straight and are 3-and-9 at Wrigley Field.
