Despite Dempster's second consecutive quality start, in which his only blemish was a second-inning leadoff single to Jose Lopez and subsequent two-run home run by Franklin Gutierrez, the Cubs were powerless against Mariners left-hander Jason Vargas, who tossed seven shutout innings and struck out seven.
In the fifth inning, Alfonso Soriano led off with a double and took off from second base when Tyler Colvin hit a hard line drive to left field.
"I thought the ball was going to drop, and drop on, like, one bounce to the left fielder," Soriano said.
He thought wrong. The ball was caught, Soriano was doubled off to squelch a potentially big inning, and Cubs manager Lou Piniella was flummoxed once again by his team's inability to click from night to night.
Tuesday's shutout marked the club's second in its past three games, and the other game was a win in Anaheim in which Chicago scored 12 runs.
"We wasted a good pitching performance on our side," Piniella said. "You give up two runs, your pitcher is doing his job. ... We only had four or five chances to score runs and we just didn't get it done. We've had trouble scoring runs this year."
The Cubs saw another chance go down the tubes in the seventh when Geovany Soto worked a two-out walk and moved to third on a Soriano single, but Colvin's grounder was stopped by Mariners first baseman Mike Carp on a diving play.
And in the eighth, with runners on first and second and none out, Marlon Byrd hit into a double play against Mariners reliever Brandon League. Pinch-hitter Chad Tracy then left a runner on third with an inning-ending flyout.
The Cubs made it interesting yet again in the ninth against Seattle closer David Aardsma, when a walk and a Soriano single -- his third hit of the night -- put runners on the corners, but Colvin struck out to end it.
The Cubs took nothing away from the mastery of Vargas, who earned his fifth consecutive quality start, his sixth victory of the season -- fourth in a row -- while lowering his season ERA to 2.66.
"He was locating all of his pitches," said Cubs second baseman Ryan Theriot. "It goes to show when you're a pitcher, if you can hit your spots and stay consistent hitting spots, you can not only get some strikeouts and win games but go deep into games like that. He was really just throwing two pitches, and he kept us off balance with two pitches.
"You can't take anything away from Vargas. He did a good job."
And so did Dempster, who tossed the 11th complete game of his career and first since Sept. 29 against Pittsburgh. The righty has pitched six or more innings in 14 of his 15 starts this season.
"We saw him in Spring Training, and he was unhittable in Spring Training," said Mariners skipper Don Wakamatsu. "The game plan today was to attack him early. He throws a lot of first-pitch fastballs, and you don't want to that slider and split. You saw him get stronger and stronger. He competed all night and I thought he threw a heck of a ballgame."
But it wasn't a win, and the Cubs keep wondering what they need to do to break out of a prolonged funk.
Dempster offered one way to get out of the rut -- start a new winning streak Wednesday.
"We've got to plug our way through it," he said. "It's tough times, and you've got to find a way to dig down deep and do the best you can. Sometimes some of the greatest opportunities are disguised as overwhelming obstacles.
"We've got a good opportunity to bounce back tomorrow and go out there and win a game."