Dempster (2-0) picked up the win, giving up three runs, including two on Griffey's blast in the third. Dempster scattered five hits and walked five over six-plus innings, striking out three. He's making the conversion from closer to starter look easy.
"It was a battle out there," Dempster said. "I didn't have the command I've had the last couple games. With the wind blowing out like that you try to minimize the damage as much as possible."
He still has some things to work on.
"I feel like I'm throwing the ball good, and I want to keep on improving every time," Dempster said. "I want to be more aggressive, throw more first-pitch strikes, and I feel if I do that, I have a good chance to win the ballgame."
"He had a very respectable spring, and it's carried over here early in the season," Cubs manager Lou Piniella said of the right-hander.
The win may be costly as Alfonso Soriano left in the first after he strained his right calf catching the final out of the Reds' half of the inning. Soriano underwent an MRI Tuesday night, and the team expected results Wednesday.
DeRosa, who moved from second to left when Soriano was hurt, hit a two-run homer in the second to erase the Reds' 1-0 lead. Kosuke Fukudome singled to lead off, and DeRosa followed with his third homer off a 3-1 pitch from Aaron Harang (1-2).
Griffey's homer made it 3-2 in the Reds third. He now ranks sixth on the all-time home run list behind Sammy Sosa.
The Cubs answered in the fifth. Mike Fontenot doubled to lead off, and Ryan Theriot walked to set up Lee, who notched his fifth homer. Last year, Lee hit just six homers before the All-Star break, and did not notch his fifth until June 1.
"He's stroking it," Piniella said. "He's on the ball. He's stroking it and driving it. I wish I could hit my driver that good on the golf course."
The Reds added a run in the seventh on Jeff Keppinger's fielder's choice with the bases loaded. It could have been worse for the Cubs, but Fontenot made a great stop of the ball, and flipped to Theriot at second. Even though he couldn't complete a double play, it was a huge stop. Lee and Theriot did turn two on Griffey's grounder to end the inning.
"That one inning we still had a chance to get the victory if Fontenot hadn't made that play up the middle," Reds manager Dusty Baker said. "That was a heck of a play. That was a game-saver for them right there."
"Fontenot made an unbelievable play up the middle," Dempster said. "That's game-waving right there. That's probably the most important part of the game."
It helped when the Cubs padded the lead on a RBI double by Aramis Ramirez and a RBI single by DeRosa in the seventh, and a two-run homer by Theriot in the eighth.
It's unusual for the wind to be blowing out on a chilly night in April at Wrigley. The Cubs were happy it was in their favor.
"We thought about it today during [batting practice] -- there weren't too many baseballs left when we got done with batting practice, and I'm sure Cincinnati felt the same way," DeRosa said. "All in all, it was a good team victory."