"I was hitting it for myself," Lee said with a smile. "I'm a father, too."
Lee's three-run blast in the bottom of the ninth broke a 3-3 tie, allowing the Brewers to complete a three-game sweep of the Indians.
It was the latest in a series of home comebacks for the Brewers, who have trailed in 20 of their 24 victories at Miller Park this season. Geoff Jenkins hit a two-run single in the bottom of the ninth to beat Cleveland on Saturday.
"They don't fold up when they get behind a little bit," Brewers manager Ned Yost said. "They keep after it."
With the victory, Milwaukee has climbed back to the .500 mark for the first time since May 30. After breaking an eight-game losing streak earlier this month, the Brewers have won nine of their last 13.
"We bounced back from that little streak really well, and have been playing pretty good baseball," Yost said.
That certainly isn't the case for the Indians, who have lost five straight series and 10 of their last 13 games.
"Any time you lose games late like that, it's just all the tougher," Indians manager Eric Wedge said. "They took it to us late."
Gabe Gross led off the ninth with a double, and went to third on a sacrifice bunt by Rickie Weeks. Wedge had Rafael Betancourt intentionally walk Corey Koskie to get to Lee.
"Raffe is better against right-handers," Wedge said. "We put Koskie on, Raffe has handled Carlos good in the past. We just gave him a pitch up he could hit."
Betancourt (0-3) took the loss for Cleveland. Derrick Turnbow (4-3) pitched the ninth to get the victory for Milwaukee.
The Brewers squandered a chance to take the lead in the eighth, putting runners on first and second with one out but failing to score. Chad Moeller popped out, and pinch hitter Jeff Cirillo hit a deep fly ball that was caught at the warning track in left field to end the inning.
Cirillo jumped in frustration after rounding first base and appeared to hurt his ankle. Yost said he didn't know how serious the injury was.
Milwaukee's Prince Fielder tied the game at three with a leadoff solo home run in the sixth, his 13th homer of the year.
"I'll have a hard time sleeping for the 3-2 change-up down the middle to Fielder," said Cleveland starter Paul Byrd, who gave up three runs and seven hits in six innings. "It was right down the middle. It was the difference in the game."
The Brewers had to come from behind after a shaky start by rookie Zach Jackson. Yost pulled the highly regarded left-hander after he allowed eight hits in the first three innings.
"I was a little bit thrown off by that," Jackson said of being taken out. "But 80 pitches in three innings? That's unacceptable."
Geremi Gonzalez relieved Jackson in the fourth and allowed a leadoff triple to Grady Sizemore. Sizemore later scored on a sacrifice fly by Eduardo Perez, giving Cleveland a 3-2 lead.
Yost allowed Jackson to bat in the third, and he hit a sharp single to center for his first major league hit. Koskie then hit a two-run homer to right, tying the game at two.
Despite being hit hard, Jackson kept the damage to a minimum, allowing only two runs -- one of which came on a wild pitch -- as the Indians stranded seven runners in the first three innings.
"We missed opportunities early," Wedge said. "We were horrible with runners in scoring position."
With two on and no out in the third, Jackson allowed an RBI single to Jhonny Peralta, scoring Perez from second base to go up 2-0.
Ronnie Belliard then singled to load the bases. But Jackson got Franklin Gutierrez to pop out, struck out Tim Laker, and got Byrd to ground out to end what would become Jackson's final inning.
Jackson, who earned his first major league victory at Cincinnati on June 12, allowed the first run of the game in the second inning, uncorking a wild pitch that allowed Belliard to score from third.
Yost hasn't decided who will start Tuesday's game against Detroit. Promising right-hander Carlos Villanueva was originally scheduled to start the game, but veteran Rick Helling could return from an elbow injury. ... Wedge said it would be "optimistic" to expect outfielder Casey Blake to return in two weeks. Blake was placed on the 15-day disabled list with a strained left oblique muscle Friday. ... Lee stole two bases in the first inning. ... Sunday's attendance was 43,391, putting the Brewers over 1 million in attendance for the season.