The Indians struck quickly against 325-game winner Maddux, whose only previous appearance at Jacobs Field was with Atlanta in Game 5 of the 1995 World Series.
Sizemore (.295) singled, stole second and scored on Todd Hollandsworth's single. After Jhonny Peralta walked, Victor Martinez (.294) singled in Hollandsworth. A two-out double by Ron Belliard (.292) made it 3-0.
"I pretty much lost it for us in one inning. It took me too long to settle in," said Maddux (7-7, 4.83 ERA). He is just 2-7 with a 6.83 ERA over his last 10 starts -- after going 5-0 with a 1.25 ERA to open the season.
"Hollandsworth hit a good pitch, but other than that, I was up, I was down and falling behind in the count. I'm not getting away with many mistakes. I didn't pitch badly, except for the first inning."
Maddux then got locked in, retiring 11 straight Indians until Sizemore lined a pitch into the Cubs' bullpen in right for his 13th homer and 4-1 lead in the fifth.
"It was right down the middle," said Maddux with disgust.
Meanwhile, Lee (6-5) allowed two runs (one earned) over 7 2/3 innings to continue his dominance in interleague play. The left-hander improved to 5-0 with a 3.31 ERA in eight career starts against National League teams.
Two errors on one play by second baseman Belliard helped Chicago score an unearned run in the second to get within 3-1.
Aramis Ramirez (.256) hit his 13th homer, over the wall in center, to make it 4-2 in the sixth.
Both Lee and Sizemore admitted being a bit in awe of Maddux, yet were thrilled to beat the right-hander.
"Maddux is one of the guys I've tried to be like," Lee said. "It's something I can always say, I had a chance to beat Greg Maddux. He's one of the best."
Added Sizemore: "I grew up watching the guy. I kind of felt like going out and asking for his autograph before I went up to hit.
Maddux gave up four on seven hits and one walk, striking out four over 7 1/3 innings.
"Greg threw the ball great, especially after the first inning," manager Dusty Baker said. "He hung a breaking ball to Belliard, and the home run to Sizemore was on an 0-2 pitch. They were the only two mistakes he made."
Jacque Jones (.296) went 3-for-4 for Chicago. After walking in the fifth, he was thrown out trying to score from first on a double to left by Henry Blanco.
Before the game, the Indians designated Jason Johnson for assignment. The right-hander, signed as a free agent in December, was just 3-8 with a 5.96 ERA in 14 starts, allowing 108 hits in 77 innings.
Cleveland also optioned right-hander Jeremy Guthrie to Triple-A Buffalo, recalled right-hander Edward Mujica from the Bisons and purchased the contract of utility man Joe Inglett from Buffalo.
Shapiro said that left-hander Jeremy Sowers, the Indians' first-round draft pick in 2004, will take Johnson's spot in the rotation, making his major-league debut Sunday against Cincinnati.
"I would caution to think that he's going to come in here, put the team on his back and carry us," Shapiro told reporters.
He said that "several clubs" have expressed interest in Johnson and that he hoped to deal the right-hander in the coming days -- but that he is not looking to "pull the plug on the season," with a series of transactions.
"There are a few guys we might consider trading," he said. "But we don't have to trade anybody. Our primary goal right now is to make this team better."
The Cubs also were busy during pregame as Kerry Wood threw a simulated game. The right-hander, 1-2 with a 4.12 in only four starts this year, went on the disabled list June 7 because of shoulder problems. He made 70 pitches Tuesday, but reportedly struggled over the final 10 throws and stopped.
"We'll try to get him over the hump," Baker said. "We have to do what's best for him and what's best for us. Hopefully, that will come together simultaneously at some point."
Cubs first baseman Derrek Lee, out since April 21 with a broken right wrist, took batting practice on the field for the first time on Tuesday. "It's great to see him out there," said Baker, adding that he is not sure when the slugger may return to the lineup.
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