Mark DeRosa and Cedeno each drove in two runs to back Dempster and lift the Cubs to victory, which dropped the Cardinals to seven games back in the National League Central. Milwaukee is in second, four games behind Chicago.
"I know it's getting down to the last month, and you don't want to be scoreboard watching too much," DeRosa said, "but at the same time, when you're playing teams that are on your tail, to take the series is important."
The Cubs must be wondering why they didn't convert Dempster to a starter before this season. Now 13-5, he struck out six and limited St. Louis to six hits over 6 2/3 innings to improve to 11-2 at Wrigley Field.
"He's a strike-thrower," St. Louis' Skip Schumaker said. "We knew that coming in. He can throw three pitches for strikes, and he's got really good control of all three of his pitches."
The right-hander, who was the Cubs' closer for the past three seasons, says he's a better pitcher now because of experience.
"I don't panic in big situations," Dempster said. "If you try to simplify things and execute one pitch at a time -- I know it's a cliche, and it's repeated over and over -- but it really just comes down to that."
Pitching in the ninth inning in front of sellout crowds at Wrigley Field has taught him how to harness his adrenaline. He received a rousing ovation when pulled in the seventh inning from the crowd of 41,268.
"It's been awesome here, really from Day 1," Dempster said. "It's been a unique place to play. I've been here five years, and it's never felt like this. And I've played in other cities, and it's never felt like this. It's a tribute to our fans and how great they are and how excited they are about our team and how much fun the guys are having."
Aramis Ramirez set the tone early, hustling for the Cubs' first run. He singled to lead off the second and scampered to second on a fielding error by right fielder Ryan Ludwick. Ramirez advanced on Jim Edmonds' fly ball to deep center and scored on DeRosa's sacrifice fly.
"You've got to take advantage of every mistake they make," Ramirez said.
The Cardinals had runners at second and third in the fourth with two outs, but Edmonds made a diving catch of Carpenter's fly ball to end the inning.
"Who knows? If he doesn't make that catch, who knows where we are?" Dempster said. "That was definitely a game-saving catch."
It wasn't the only one. Dempster's hockey background paid off in the St. Louis fifth when he snared Ludwick's liner with a kick save on the mound and recovered in time to throw him out, stranding two more. First baseman Derrek Lee was somehow able to grab Cedeno's off-balance throw from short and still make a swipe tag on Yadier Molina -- just getting his foot while falling to the ground -- in time in the sixth. Kosuke Fukudome made a great diving catch in the ninth.
The Cubs sent eight batters to the plate in a five-run sixth. Alfonso Soriano doubled to lead off and scored one out later on Lee's single. Ramirez walked, and Chris Carpenter (0-1) threw two pitches to Edmonds, the second low and inside. Carpenter then called the catcher to the mound and left the game with a strained bicep.
Ron Villone came in, and Edmonds hit a ball that scooted through second baseman Adam Kennedy's legs, allowing Lee to score. DeRosa added an RBI single, Geovany Soto singled, and both scored on Cedeno's double to make it 6-0.
The Cubs got guys on, got 'em over, and got 'em in -- and got the Cardinals out. Now, they have to maintain that level of play for the final 44 games.
"We like our ability to come to the ballpark, and we know we're going to win that day," Dempster said. "It's not going to happen every time -- nobody has ever won every game of the season. But we don't think we're going to win, we know we are. We have a lot of confidence in ourselves and our ability. At the same time, we don't take anything for granted.
"We have a long way to go, but we feel really good about where we're at right now."
Piniella will make sure the players remember they're on a business trip, not a mini vacation as they begin a six-game road trip on Tuesday against the Braves. They have three games at Atlanta, then Miami next weekend.
"I know before we go to Florida -- I don't like to talk to the team, but I will say a couple words to them about being ready to play and getting your rest," Piniella said.
"Sometimes," DeRosa said, "you have a tendency when you go down there and you're staying in a nice hotel and you've got the beach, sometimes you're lying on the beach and you forget you have [batting practice] in two hours. I don't think anyone forgets the fact we're down there for a reason. We're professionals."
And there's still work to do.