The Cubs will try for a four-game sweep Thursday.
After arriving at Miller Park this week with a tenuous edge over Milwaukee in the division, Chicago now leads the Brewers and St. Louis by four games.
"Games in your own division are huge. Games in your own division with teams that are right behind you, come in here one game up, it could have easily turned around and been the other way," Dempster said. "We knew we had to play good baseball."
Dempster (12-4) struck out nine and gave up one run and five hits. He won consecutive road starts in the same season for the first time since 2001 as the Cubs improved to 25-30 away from home this year.
"I know the road's different, everything's different," Dempster said. "Notoriously, teams don't play as well on the road and individuals usually don't do as well on the road, but for me, I feel like I've been pitching well on the road."
The All-Star took the mound for the eighth, but was pulled to get an ovation from the large Cubs contingent at home in "Wrigley North" following the solid outings of Ted Lilly on Monday and ace Carlos Zambrano on Tuesday.
"I was gassed," Dempster said. "It was a great ovation, always nice."
The Brewers have lost a season-high four straight at home. Chicago has handled Milwaukee's top starters so far, getting the better of reigning AL Cy Young Award winner CC Sabathia on Monday, four-time All-Star Ben Sheets on Tuesday and emerging left-hander Manny Parra (9-4) on Wednesday. The Cubs have 20 runs and 40 hits in the series.
"They're hitting pitches they're getting fisted on. They're getting them over the infield or hitting it up the middle," Parra said. "I don't know how really to defense that. Right now they're on fire."
Soriano had three hits and two walks, and is 6-for-12 in the series. He's also scored five runs and stolen three bases, helping Chicago improve to 7-2 in its last nine at Miller Park.
"That's my game. That's what I play. I play very aggressive on the bases and very aggressive at home plate," Soriano said. "The most important thing, I feel healthy. When I feel healthy, I've been able to do what I'm doing now."
Soriano, who came off the disabled list last week after missing six weeks with a broken left hand, got the Cubs going in this game, too, scoring in the first inning when Parra threw a wild pitch on a two-out strikeout.
"I felt the presence of Soriano in our lineup would mean a lot to us from an offensive standpoint," Cubs manager Lou Piniella said. "And it has. You can see the difference in production."
Up 2-1, the Cubs opened a comfortable lead in the sixth inning when Dempster and Soriano singled before Ryan Theriot's triple chased Parra.
Prince Fielder hit his 21st homer in the bottom half for the final margin.
Again the Cubs struck first, even after a two-out strikeout. With runners on the corners in the first inning, Johnson fanned on a pitch that bounced in front of the plate and squirted through catcher Jason Kendall.
Johnson turned to walk back to the dugout before realizing what happened, but even with the late jump he managed to make first base after Fielder couldn't handle Kendall's throw.
"I think I heard the ball hit one of the signs in the back and that's when I knew the ball had gotten past him," Johnson said. "I just tried to get down there as fast as I could."
Soriano scored on the play and made an emphatic safe call after watching Johnson reach first. Mark DeRosa followed by flaring an RBI single.
Milwaukee cut it to 2-1 in the bottom of the first when Dempster made his only mistake by uncorking a wild pitch that scored Ray Durham, who led off with a double and tagged up to reach third.
But the Brewers fell to 0-for-15 with runners in scoring position in the series and are 3-for-60 in the last eight games.
"We've faced two All-Star pitchers in the last two days," Milwaukee manager Ned Yost said. "You can talk about it all you want with runners in scoring position. Those are good pitchers. Those are very, very good pitchers, and that stuff happens when you face All-Star pitchers."
Cubs starter Rich Harden (0-1, 1.04 ERA) faces Dave Bush (5-8, 4.51) in the finale. ... The Cubs have left 34 runners on base in the series despite the offensive production. ... Sabathia bought a full-page ad, worth $12,870, in the Cleveland Plain Dealer's Wednesday edition, thanking the fans for their 10 years of support. Sabathia was traded to Milwaukee just before the All-Star break.