Celtics claw out a Game 7 they never trailed, and other observations as they beat the Heat for a spot in the NBA Finals

MIAMI — The Heat needed just three minutes to wipe away most of a 13-point deficit in Game 7 of the conference finals, and as Jimmy Butler rushed upcourt with less than 20 seconds left and his team somehow trailing by only two, he decided he wanted it all.

“When he shot that,” Celtics forward Jaylen Brown said, “I was like, ‘Man, what the hell?’ ”

With Al Horford backpedaling, Butler pulled up for a potential go-ahead 3-pointer. But the ball skidded off the front of the rim, and the Celtics eventually escaped with a 100-96 win that sent them to the NBA Finals for the first time since 2010.

Boston, which led by 17 points in the second quarter and never trailed Sunday, will visit the Golden State Warriors in Game 1 on Thursday night.

When the final buzzer sounded, players from Boston’s bench streamed on the court in celebration. Horford, who will make his first Finals appearance of a 15-year career, collapsed as he was overcome by emotion, before his teammates came and picked him up.

In a spontaneous combustion of emotions, Celtics center Al Horford (42) celebrates with teammate Aaron Nesmith as Jayson Tatum celebrates with Luke Kornet after the final buzzer of Sunday's 100-96 victory over the Miami Heat in Game 7 of the NBA Eastern Conference Finals.Matthew J Lee/Globe staff

Jayson Tatum had 26 points and 10 rebounds to lead Boston. Butler, who played the entire game, had 35 points, but will probably most remember the three he failed to get.

Observations from the game:

⋅ Two free throws by Marcus Smart gave the Celtics a seemingly comfortable 98-85 lead with 3:35 left. But the Heat responded with an 11-0 run, mostly by attacking for layups, and some of Boston’s old flaws resurfaced. Smart missed a trio of 3-pointers, and a wayward Brown drive resulted in a charge, giving Miami possession down by five.

Suddenly, a disastrous ending was on the table. Max Strus drilled a 3-pointer with 44.4 seconds left to pull the Heat within 98-96. After Smart missed a layup inside, Butler grabbed the rebound and dribbled upcourt. He is not an excellent 3-point shooter, but he is one of the most clutch players in the game today.

“I didn’t know what he was going to do,” Horford said. “It seemed like he was going to go for the shot, but I had to make sure that I stayed solid, and when he pulled up for the three, I was like, let me contest the best way that I can. He got a good look at it, and it was nerve-racking.”

Smart was fouled and hit two free throws with 11.4 seconds left, and Strus missed a pair of 3-pointers in the final seconds.

⋅ Tatum won the first ever Larry Bird Trophy for the conference finals MVP. He averaged 25 points, 8.3 rebounds, and 5.6 assists over the seven games while shooting 47.6 percent from the field. He didn’t really have the dominant games that have become his signatures, but he was steady, and he worked his way around constant double teams and consistently made the proper play.

“A guy that’s carried us through the season,” Udoka said. “He asked a lot to be put on his shoulders, and he delivered.”

⋅ The Heat were undefeated at home in the playoffs entering the conference finals. They went 1-3 against Boston, including a pair of blowout losses.

And this is nothing unusual for the Celtics during these playoffs. They’re 7-2 on the road, an incredible run. That should give them plenty of confidence against the Warriors, who will have home-court advantage.

“That just shows the resilience we have,” Smart said, “that we can come into somebody’s building and tear it up.”

Heat forward Jimmy Butler (22), scoring over Celtics center Al Horford, wound up with 37 points in Game 7.Matthew J Lee/Globe staff

⋅ Robert Williams really labored through this one, and is clearly not right as he battles continued knee soreness and swelling related to his March knee surgery and the bone bruise he suffered in the semifinals.

He played just 15 minutes, and had 2 points and 3 rebounds. In one second-half sequence, he caught the ball inside and was stripped before being overpowered inside for a layup. When he’s right, that’s a dunk and a blocked shot.

“It’s not going to be the same as this year, but what he gave us is valuable,” Udoka said. “He gave us exactly what we needed. Kudos to him for pushing through it.”

He and Smart could use these next couple of days of rest more than anyone.

⋅ From tossing the ball into the air at the final buzzer to collapsing to the court in apparent disbelief moments later, Horford was a picture of joy after this win. He turns 36 years old this week, and this will be his first Finals appearance.

Last season was essentially a lost year for him as he was shut down by the Thunder so the team could focus on its younger players. He never knew if he’d get another real chance, but it’s here.

“I just didn’t know how to act out there,” he said, smiling. “Just caught up, excited, a lot of hard work. I’ve been a part of a lot of great teams, a lot of great teammates, and I’m so proud of this group.”

Horford was a defensive menace during the opening quarter Sunday. He had an incredible block when Max Strus challenged him for a dunk, came up with a nice strip on a Victor Oladipo drive, and in between provided real resistance whenever the Heat looked to attack.

There was no denying the phenomenal job Celtics head coach Ime Udoka did, leading his team to the NBA Finals in his inaugural season.Matthew J Lee/Globe staff

⋅ This is a substantial step in Udoka’s first year as a head coach. This team was in 11th place in January, in danger of missing the playoffs altogether. But Udoka remained steady through it all and deserves plenty of credit for this ascension.

“He didn’t want it to be easy,” Smart said. “He didn’t cry about the circumstance. He didn’t cry about where we were in the standings earlier this year. He just wanted to keep going.”

⋅ Heat guard Tyler Herro was cleared to play after missing three games because of a groin strain, but it certainly appeared that head coach Erik Spoelstra was viewing it as a break-glass-in-case-of-emergency situation, as he went with guards Oladipo and Gabe Vincent as his first two subs. Herro played one first-half stint, was ineffective, and never played again.

⋅ Strus appeared to pull the Heat within 56-54 on a 3-pointer with 11:03 left in the third. But a few minutes later, it was announced that a review had determined Strus stepped out of bounds before taking the shot.

Flips such as this one are usually related to the shot clock. This was extremely rare, and it ended up being significant.

Celtics claw out a Game 7 they never trailed, and other observations as they beat the Heat for a spot in the NBA Finals

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