"I was terrible. I wasn't pounding the strike zone and walked entirely too many guys. If I just throw like I can, I feel like we had a good chance to win today. I just didn't get the job done," Dumatrait said. "Today, that was all on me."
The Cubs have taken eight of the nine meetings with the Pirates this season.
Adam LaRoche hit a two-run homer and drove in three runs for the Pirates.
Cubs starter Jason Marquis (2-3) won for the first time since April 19, allowing two earned runs on four hits in six innings. Bob Howry, Carlos Marmol and Kerry Wood finished with three scoreless innings. Wood pitched a perfect ninth for his 10th save.
"I thought Jason threw the ball real well after LaRoche's home run in the first inning," Mark DeRosa said. "He was able to really keep us in the game and allow us to get back in it and eventually take the lead. A lot needs to be credited to the pitchers for allowing us to scrap our way and grab four runs."
Dumatrait (1-2) lasted 4 2/3 innings. He walked the first three batters of the third, and Soriano's fly and Cedeno's single tied it at 2 after LaRoche's two-run homer in the first.
Fukudome led off the fourth inning with a walk, took third on a double steal after DeRosa's single and come home on Johnson's go-ahead fly.
Dumatrait was pulled after Fukudome's two-out RBI single, which followed two more bases on balls.
Before the game, the Cubs placed PH Daryle Ward on the 15-day disabled list with a bulging disc in his back and purchased the contract of OF Micah Hoffpauir from Triple-A Iowa. Hoffpauir struck out as a pinch hitter in the fifth. ... Despite owning the second best record in baseball, Cubs manager Lou Piniella is remaining cautious. "I think we have a chance. A lot of baseball to be played, a lot of things can happen. Like I said, the division has gotten tougher, the National League as a whole, we're little bit more of a marked team and I think for people to make those conclusions if they feel that good about it, they should load up in Vegas, but I don't feel that way," Piniella said.