Redd scored 16 of his 21 points in the first quarter and the Bucks started fast before holding off a late rally to beat the Miami Heat 98-83 on Monday night.
"I was having some fun," Redd said. "I took the challenge of Dwyane Wade and tried to contain him. We were just determined to try to set the tone."
Redd had four 3-pointers in the opening quarter to score the most points allowed in a period this season by a Heat opponent.
"We had such a big lead that they exerted a lot of energy trying to get back in the game," Bogut said. "Thankfully, we held out."
Mario Chalmers had 20 points, eight assists and seven rebounds and Wade added 15 points for the Heat, who lost their third straight game.
With Wade struggling early for the third consecutive game, the Heat scrambled to find points. Wade, who began the game leading the NBA in scoring, finished 5-for-16 from the floor.
"We can't put it all on Dwyane," Heat forward Udonis Haslem said. "Someone's got to pick their game up somewhere."
After losing at Memphis a day earlier, the Heat looked lethargic from the start against Milwaukee.
Redd's fourth 3-pointer of the first quarter put the Bucks ahead 27-15. As the Heat struggled to generate any offense in the halfcourt, Milwaukee made five 3-pointers in the opening period and forced the Heat to score out of their inept halfcourt offense.
"The first half of the first quarter was pretty ugly for us," Heat coach Erik Spoelstra said. "Offensively, we just couldn't get the ball to go in. And then defensively, we had breakdowns and they got us on the offensive glass and jumped out to a big lead."
And the Bucks didn't relent.
Villanueva capped a 13-2 start to the second quarter, converting a three-point play to stretch Milwaukee's lead to 40-21. The Heat trimmed the deficit to 68-50 on a jumper by Wade midway through the third quarter, but spotty defense and bad shot selection by Miami -- including an airball on a long 3-point attempt by Wade -- allowed the Bucks to build back their lead.
"When you go on the road, you've got to be able to guard people," Bucks coach Scott Skiles said. "You've got to be able to guard people to try to win. Tonight we did. Maybe we can build off of this."
Chalmers stole the ball from Charlie Bell and turned it into an uncontested dunk, clenching his fist and screaming in celebration to end the third quarter with Miami trailing 77-65.
Miami got as close as nine points after Daequan Cook made a 3-pointer with 3:03 remaining. But Milwaukee would answer, with Villanueva scoring four straight points and the Heat going cold.
Miami will have three days to regroup before trying to end its slide at home against the Los Angeles Lakers.
"We have to stay together," Spoelstra said. "There's a lot of teams in the Eastern Conference that are going through a tough stretch right now or have been through a tough stretch. Now we're one of those teams. And it's not how you got into there, it's how you respond."
Wade was called for a technical foul after he yelled at the referee from the bench with 1:21 left in the second quarter. ... Haslem, who missed the Heat's game at Memphis on Sunday to attend his grandmother's funeral, was back in the starting lineup. ... Spoelstra said before the game that he thought center Jamaal Magloire's actions Sunday didn't merit an ejection. "It looked pretty innocuous to me," Spoelstra said. Magloire was ejected for head-butting Memphis' Darko Milicic as they fought for position on an inbound.