Dempster (2-0) gave up one run on seven hits in 7 2-3 innings. He struck out four and walked one to improve 9-1 in his last 11 starts against Milwaukee. His effort picked up the Cubs who had lost five of the last six games.
Dempster cooled off the Brewers who had outscored the Pittsburgh Pirates 36-1 during a three-game sweep, including Thursday's 25-hit, 20-0 pounding. He didn't allow a runner past second until the seventh when the Brewers pushed across a run on Craig Counsell's pinch-hit double.
Dempster caught a huge two-run break in the bottom of the first.
Crew chief John Hirschbeck reviewed Prince Fielder's blast to deep center which appeared to land behind the yellow line atop the wall. Second base umpire James Hoye ruled it a double instead of Fielder's second home run of the season. Macha asked for the review which barely took a minute. Hirschbeck let the call stand. Ryan Braun stayed at third and Casey McGehee ground out to third to end the inning and preserve the Cubs' 2-0 lead.
Mike Fontenot's one-out RBI-single in the fifth, the third consecutive hit, forced Brewers manager Ken Macha to pull Jeff Suppan (0-1) who was booed off the field. Koyie Hill singled off reliever Claudio Vargas to drive in Marlon Byrd.
Each position player had at least one hit off Suppan who gave up six runs and 10 hits over 4 1-3 innings.
Ryan Theriot tripled to drive in a run in the fourth.
Fukudome hit Suppan's first pitch of the third inning into the right-field bleachers.
The Cubs pushed across two runs in the first.