"Chris is accomplished and he's been working hard at it," coach Pat Riley said. "You can see the improvement in the game and the confidence."
Quinn shot 8-of-13 and added four rebounds, four assists and four steals.
"It's been just two years of his own work and perseverance and waiting and patience, being loyal to his work ethic," Riley said. "And when he gets an opportunity, this is when he can shine."
It was the second time in six days the Heat defeated the Bucks, who fell to 6-28 on the road. The two victories over Milwaukee are the only ones Miami has in its last 13 games. The win also marked the first time the Heat defeated an opponent twice this season.
"It was one of the old grind-out games," Riley said. "They're desperate as hell, obviously because they are right on the brink of being eliminated. It was a fun game to coach and to watch, even though it wasn't one of the free-flowing games."
Quinn drew a foul on Mo Williams with 45 seconds left and knocked down two free throws to give Miami a 74-71 lead.
Ricky Davis' shot missed, giving the Bucks an opportunity for another possession, but Stephane Lasme corralled the offensive rebound and passed to Daequan Cook with 6 seconds left. Cook was fouled, and he calmly knocked down two free throws to seal the victory.
Five of Miami's nine players that saw action played in the NBA Development League earlier this month. Lasme, Blake Ahearn and Kasib Powell each recently signed 10-day contracts and combined for 10 points and eight rebounds.
Mo Williams threw an alley-oop to Andrew Bogut to pull the Bucks within 62-59, but Quinn responded with a 3-pointer on the ensuing possession to halt Milwaukee's momentum.
"We just kind of went through the motions and thought it was going to be easier than it was," Bucks coach Larry Krystkowiak said.
Leading 67-64, Quinn made a driving layup past Mo Williams, who fouled Quinn on the play with less than four minutes left. Quinn knocked down the free throw to give the Heat a 70-64 lead.
"It was a side pick-and-roll and I went away from the screen and was able to get the shot up on the rim and it dropped," Quinn said. "It was a crucial part of the game to get that basket and I'm just glad we could get a win."
Milwaukee led 33-23 midway through the second quarter after a jumper by Redd giving the Bucks their largest lead of the half, but the Heat battled back pulling within five at halftime, 37-32.
Miami started the third quarter on a 15-3 run as the Bucks made just one of their first 13 shots.
"Defensively we did a good job and offensively we were horrible," said Bogut, who finished with 16 points and 17 rebounds.
Williams is out at least a week with a right thumb injury he suffered on March 18. He's in a hard cast and will get an MRI on Tuesday. He joins a long list of Heat players who are sidelined with injuries including Dwyane Wade, out for the year with a knee injury. Shawn Marion (back), Udonis Haslem (ankle), Alonzo Mourning (knee), Dorell Wright (knee), Marcus Banks (hamstring), and Alexander Johnson (knee) are also out. ... Anthony had a one-handed dunk over Yi Jianlian in the second quarter that brought the Heat reserves to their feet. "It definitely felt good," Anthony said. "Honestly, I couldn't stop smiling all the way down the court. If they had the camera on me, you would have nothing but my mouthguard." ... Marion received the results on his MRI today, which showed he just has back spasms. He's considered day-to-day.