If the Cubs are going to make a run, they'll need more of this from those two.
Dempster simply dominated while earning his first win since April 23, and the struggling Lee backed him with three hits as the Cubs won for the seventh time in nine games.
"He shut them down," Lee said. "He's been great all year."
As for his own performance?
"I felt some good swings," said Lee, who boosted his average from .218 to .231. "I haven't done that in a long time. Hopefully, this is the start of something."
He drove in Ryan Theriot with a single off Clayton Kershaw (4-3) in the sixth after shortstop Rafael Furcal booted his grounder. Lee made it 3-0 in the eighth with a two-run shot off Ramon Troncoso -- his sixth homer this season and 299th in all -- after Starlin Castro reached on a throwing error by Furcal.
That was enough for Dempster (3-4), who handed the Dodgers just their third loss in 15 games.
"He was locating pretty well tonight," the Dodgers' Casey Blake said. "He was mixing up the slider and splitty. We didn't have any opportunity to get innings going."
He shut down a team that came in with a major league-leading .288 average against right-handers, striking out seven while walking one and retiring his final 13 batters after going 0-4 in his previous five starts.
He walked off the mound to loud cheers after retiring the side in the eighth and had no problem turning it over to Carlos Marmol, who struck out two in a perfect ninth for his 10th save in 12 chances.
"It's nice to see your closer go out there who's been dominating," Dempster said. "I'm not about trying to pad my stats with a shutout."
The Dodgers got shut out for the sixth time and wasted another strong effort by Kershaw, who took the loss after winning his previous three starts even though he allowed one unearned run and four hits over six innings.
The left-hander did not allow a hit until Lee lined a one-out double to left center in the fourth, just past Manny Ramirez. Marlon Byrd, who came in on a 2-for-23 slump, then blooped a single to right to put runners on first and third, but Alfonso Soriano struck out and Xavier Nady grounded to third to end the threat.
The Cubs finally broke through in the sixth, after Furcal's first error.
Back after missing 24 games with a strained left hamstring, he booted the ball trying to backhand Theriot's leadoff grounder and Chicago took advantage.
Theriot stole second with one out and came around on Lee's line-drive single to center, making it 1-0.
"As a team, you can accomplish a lot when guys start to do everything -- the little things, as well as the big things," Dempster said.
Byrd lined another single to center, putting runners on first and second, but Kershaw escaped more damage by retiring Soriano on a pop and Nady on a liner to center following a visit by pitching coach Rick Honeycutt.
Furcal made another error in the eighth when his throw pulled first baseman James Loney off the bag, allowing Castro to reach. Lee then drove a fastball from Trancoso out to right, making it 3-0.
"It was not a pretty day for me," Furcal said. "I'm very disappointed the way I played."
The Dodgers placed left-handed reliever George Sherrill on the 15-day DL because of tightness in his mid-back. ... Carlos Zambrano will likely be back in the Cubs' rotation next week after throwing 75 pitches in a simulated game on Monday. Manager Lou Piniella says Zambrano will be available for short relief beginning on Thursday and probably start during the three-game series at Pittsburgh early next week. ... Struggling 3B Aramis Ramirez was out of the Cubs' lineup for the third time in four games because of a sore left thumb. Jeff Baker started in his place.