"I felt like I took it up a level in the fourth quarter," Butler said. "If that needs to happen every game, I've got to be able to do it. But we've got so many guys capable of doing it for us."
With the victory, the Heat are now 3-1 overall against the Bucks this season. Miami -- fresh off a sweep of the Indiana Pacers in the first round -- also improved to 5-0 in the playoffs.
Heat guard Goran Dragic added 27 points, six rebounds and five assists. Bam Adebayo, who finished second behind New Orleans Pelicans forward Brandon Ingram for the NBA's Most Improved Player Award, had 12 points, 17 rebounds and six assists for the sixth-seeded Heat.
Sharpshooter Tyler Herro finished with 11 points on 3-of-11 shooting for the Heat. Jae Crowder added nine points and nine boards in 35 minutes.
Bucks superstar Giannis Antetokounmpo notched 18 points, 10 rebounds and nine assists, but his struggles from the free throw line marred his well-rounded outing. The reigning NBA MVP went 4 for 12 from the stripe, marking the worst playoff performance by anyone with at least 12 free throw attempts in more than three years.
"He just has to stick with his routine, stick with what he's been doing, continue to have a lot of confidence, continue to attack, continue to get to the free throw line," Bucks head coach Mike Budenholzer said. "He's going to make them. We have total faith in him."
Game 2 of the best-of-seven series is set for Wednesday.