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Heat-Bucks: 56k | 300k 
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Redd gave Milwaukee the lead for good when he snapped a 45-45 tie with a basket with 2:06 left in the second quarter, igniting a 10-0 run that gave the Bucks their first double-digit lead. Marcus Haislip had six of his seven points in the spurt.
Milwaukee held a 21-point advantage with 10:51 remaining before Miami went on a 24-8 tear, pulling within 96-91 with 3:51 to go on a jumper by Eddie Jones.
"They hit some shots and really cranked it up on the boards," Bucks coach Terry Porter said. "They just cranked it up and turned up the intensity. You know they're going to do that and we just didn't turn it up with them."
Lamar Odom cut the deficit to 100-97 with a basket with 2:01 left, but Redd was fouled on a 3-pointer and he drained all three free throws.
Former Buck Rafer Alston's 3-pointer again pulled the Heat within three points with four seconds left, but Miami ran out of time.
"Miami shot the ball extremely well down the stretch and they were able to get back into the game with big threes and we weren't making shots, so they made it a game," Milwaukee guard Damon Jones said. "I think we weren't able to get stops, we got kind of lackadaisical with the big lead and that happens sometimes."
Toni Kukoc added 17 points and Keith Van Horn contributed 11 and 12 rebounds for the Bucks, who had to stave off a late rally in their 106-104 triumph over Memphis on Friday.
"The last few games have been too close for comfort, but we managed to get a win and get it done," said Redd, who shot 7-of-15 from the field, including four 3-pointers. "Thankfully at the beginning of the year, we had a lot of nail-bitters. We won some and we lost some, but I think that's helping us now, finishing games."
Milwaukee has won three in a row overall and five straight against Miami.
Eddie Jones finished with 25 points and Odom 22 as the Heat dropped their third straight contest after a four-game winning streak. They are battling for the eighth playoff spot in the Eastern Conference.
"It is very important to win games on the road, but today we just got too far behind and just ran out of gas," Alston said. "We have to start winning on the road like we do at home if we want to make the playoffs."
Miami played without rookie Dwyane Wade for most of the second half after the guard crashed face-first into the basket stanchion in the first quarter. Wade sprained his right foot when Redd fell on top of him and left for good with 5:50 left in the third period.
"I came down wrong and then Michael Redd came down on me," said Wade, who played at the Bradley Center while at college at Marquette. "It was a big collision of all three of us. My foot was under his body when he fell, and that twisted it. It wasn't my neck. My teammates thought it was my neck, but it was my foot."