Dempster tied the team record with a 33-inning scoreless streak, pitching six solid frames and leading Chicago over the Arizona Diamondbacks 4-1 on Saturday.
Dempster matched the mark set by Ken Holtzman in 1969.
"It's pretty crazy. I think as a reliever when you do something like that it seems a little more realistic because you go out there one inning at a time," Dempster said. "To go out there start after start and not give up any runs is pretty humbling. I'm just trying to get outs and not expecting that and trying to win ballgames."
Dempster (5-3) allowed four hits and set a career best by winning his fifth straight start. He leads the majors with a 1.86 ERA.
Cubs manager Dale Sveum limited Dempster to 89 pitches. The right-hander made his second start since coming off the disabled list with tightness in his pitching shoulder.
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"When I took him out he wanted to stay, but he wasn't going to talk me out of it. That's a competitive pitcher that wanted to stay in. That was the game plan today and it worked out perfect. He got another inning in and he got to 90 pitches. The plan worked to a tee today," Sveum said.
Dempster struck out five and walked three. With the Cubs far back in the playoff race and Dempster in the last season of a four-year contract, he has become a possible trade option for contending teams.
"Like I said before, I am well aware of things going on, rumors and things like that," he said. "But I'm a member of the Chicago Cubs and I'm trying to do my best job for this team."
"I understand the business side of baseball, too," he said. "But I have not given it a whole lot of thought to be somewhere else now. I'm just enjoying playing here, winning today and being part of this run we are on."
Darwin Barney hit an RBI double for the Cubs, who have won 11 of their last 15 games.
"You don't want to come in and lose the first two games," Arizona manager Kirk Gibson. "We scored two runs in Wrigley Field in two days. That's not what we expect to do. We got to do better than that. "We're 0 for 5 with runners in scoring position, we hit in three double plays today and a couple yesterday. We struck out in key situations. That's not the way to get it done."
Cubs closer Carlos Marmol pitched a scoreless ninth for his ninth save in 11 chances. Marmol allowed a leadoff double to Stephen Drew and walked Young. Geoff Blum followed with a deep fly ball to right, but Reed Johnson made a nice running catch up against the ivy, then Marmol got pinch hitter Jason Kubel to hit into a double play to end the game.
Joe Saunders (4-6) returned after being on the disabled list with a left shoulder strain and pitched six innings. He allowed three earned runs and eight hits.
"Felt great. It was fun to get back out, start contributing again," he said. "We knew runs were going to be hard to come by against Mr. Dempster out there, he's been throwing the ball great. You just try to limit the damage and hope you get a couple breaks."
In the fourth, Alfonso Soriano led off with a single and later scored on Barney's two-out double. Three pitches later, Valbuena singled up the middle for a 3-0 lead.
The Cubs scored in the sixth on an error and Barney's double-play ball.
- The Diamondbacks optioned LHP Patrick Corbin to Triple-A Reno to make room on the roster for Saunders. Gibson said Corbin will work as a starter at Reno. He started five games for Arizona this year but had been appearing out of the bullpen of late.
- Kubel (right hamstring tightness) was held out of the starting lineup. Gibson said Kubel was still sore. Kubel was removed in the seventh inning of Friday's 8-1 loss after slipping several times on the slick field.