Dempster (13-10) gave up three hits, walked two and struck out eight for the Cubs, who shut out the Brewers in Friday's series-opener, 4-0. Andrew Cashner, Sean Marshall and Carlos Marmol held Milwaukee scoreless over the final two innings to complete the three-hitter.
"It's been a struggle to throw the ball well the last couple of times out," Dempster said. "Command was the difference tonight. The last couple times out I was leaving the ball over the middle of the plate."
Randy Wolf (11-11) was the hard-luck loser, as he gave up only Nady's home run in eight innings. Wolf allowed four total hits, walked one and struck out six for the Brewers, who fell to 2-3 on their homestand.
"I think it was probably my best game of the year, as far as my command, my stuff and comfort level out there," Wolf said.
Milwaukee threatened in the second inning, when Casey McGehee and Lorenzo Cain walked with one out. However, Dempster induced two consecutive groundouts to escape the jam.
In the sixth, Chicago's Jeff Baker doubled with one out, but was stranded after the next two batters were retired on fly outs.
However, Nady broke the scoreless tie in the seventh, when he homered to left with one out.
Cashner got into some trouble in the eighth, when he hit pinch-hitter Joe Inglett to lead off the inning. Pinch-runner Carlos Gomez stole second before Cashner walked Corey Hart with one out. But Cashner fanned Ryan Braun before Marshall struck out Prince Fielder to end the inning.
Marmol worked a 1-2-3 ninth for his 30th save.
The Brewers left seven on base...Chicago leads the season series, 9-5...Baker finished with two hits...Dempster had lost his last two starts, in which he gave up 14 runs (10 earned) in 7 2/3 innings.