Butler also recorded eight rebounds, four assists and two steals in the 128-126 Game 5 win Wednesday at Fiserv Forum. He averaged 37.6 points per game and shot 59.6% in the best-of-seven game series, which the Heat won 4-1.
"I'm just in a groove and in a rhythm," Butler told reporters. "I've been shooting the ball an incredible amount this series, but I feel like they are all shots I know I can make.
"My teammates keep telling me to shoot the ball more and attack. That's what it was."
Heat forward Bam Adebayo recorded a triple-double, with 20 points, 10 rebounds and 10 assists. The Heat, who trailed by as many as 16 points, outscored the Bucks 52-48 in the paint and 21-13 off the bench.
Forward Giannis Antetokounmpo logged 38 points and 20 rebounds for the top-seeded Bucks.
"You don't always win," said Antetokounmpo, who led the Bucks to a title in 2021. "Sometimes, other people are going to win. This year somebody else is going to win.
"We are going to come back next year, try to be better and build habits."
The No. 8 Heat, who played in two play-in tournament games to reach the playoffs, will meet the No. 5 New York Knicks on Sunday in Game 1 of an Eastern Conference semifinal series.
"We'd never been in a play-in," Heat coach Erik Spoelstra said. "In both of those games, it was great competition. We'd never been a No. 8 seed, with an opportunity to win. We wanted to embrace this opportunity.
"It has just been a harrowing 2 1/2 weeks. But our guys earned their ice."
Butler scored 11 in the first quarter and the Heat made six 3-pointers to carry a 36-33 lead into the second.
Antetokounmpo and fellow forward Khris Middleton scored 11 and 17 points, respectively, over the first 12 minutes.
The Bucks outscored the Heat 36-27 in the second, fueled by a 15-3 run, to bring a 69-63 edge into halftime. The Bucks outscored the Heat 33-23 in the third and led by 16 to start the fourth.
Neither team scored for the first two minutes of the final quarter. The Heat then scored eight unanswered, as part of an 11-1 run, cutting the deficit to eight. The Heat later added a 6-1 run to cut the Bucks lead to five with 4:01 remaining.
That run was part of a stretch that saw Butler score 12 consecutive Heat points. Butler tied the score at 111-111 with 2:11 remaining. Antetokounmpo answered with a go-ahead layup on the next shot, but Adebayo responded with a game-tying jumper about 15 seconds later.
The Bucks pushed the lead back to four with 14 seconds remaining. Heat guard Gabe Vincent hit a 3-pointer on the next possession to tighten the score.
Bucks guard Jrue Holiday made 1 of 2 free throws on the other end. Vincent then threw a precise cross-court pass over the right side of the rim, finding Butler for an alley-oop layup with 0.5 seconds remaining for the final score of regulation, which forced overtime.
The Heat went on a 6-1 run to start the bonus frame. Antetokounmpo decreased the deficit to two points with 59 seconds remaining, but Heat guard Max Strus made two free throws on the next possession. The Bucks star again cut the lead to two with 29.5 seconds remaining. The Bucks then failed to get a shot off on their final possession, resulting in an early playoff exit.
Vincent scored 22 points in the win. Heat forward Kevin Love and guard Kyle Lowry scored 15 and 10 points, respectively.
Middleton scored 33 points for the Bucks. Bucks center Brook Lopez chipped in 18 points and 10 rebounds.
The Knicks will host the Heat at noon EDT Sunday in New York.