Celtics center Al Horford falls to his knees after Boston beat Miami 100-96 in Game 7 of the Eastern Conference finals on Sunday in Miami. Nobody has played more playoff games without making the finals than Horford, who played in his 141st playoff game Sunday. Lynne Sladky/Associated Press

MIAMI — The game was over. So, finally, was Al Horford’s journey. He grabbed what would be the final rebound of the Eastern Conference finals, threw the ball skyward, sprinted to join his teammates in celebration and then dropped to his knees to slap the floor.

His time has come.

The oldest player – by six years – on the Boston Celtics’ roster will savor this trip to the NBA Finals in ways that his teammates simply cannot. He will finally play in the title series, with the Celtics set to open the matchup against the Golden State Warriors on Thursday night, one day before Horford’s 36th birthday.

“Nobody deserves it more,” Boston guard Jaylen Brown said.

Nobody in the history of the NBA has played more playoff games without making the finals than Horford; Sunday night’s 100-96 East title-clinching win in Miami was his 141st postseason appearance. When the ball is tipped in San Francisco for the start of Celtics-Warriors, that dubious distinction becomes Paul Millsap’s possession; he’s been in 130 playoff games, none in the finals.

Horford didn’t know what the moment – making the finals – would be like. Turns out, it was better than he envisioned.

“Just didn’t know how to act,” Horford said. “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. … I’m really grateful to be in this position.”

Horford had a previous three-year stint in Boston, making the East finals twice, before signing with Philadelphia and eventually getting moved to Oklahoma City. He didn’t play much for the Thunder, and they traded him last summer back to Boston – a move that worked out better than even the Celtics hoped.

His averages so far in these playoffs: 11.9 points, 9.6 rebounds and 3.5 assists while playing nearly 37 minutes per contest.

“Al could care less about the numbers,” Celtics guard Marcus Smart said. “He cares about the wins and this team. When he came back, that gave us a sense of security. We got Al back there, he’s always going to make the right play on both ends, he’s going to calm us down, he’s going to show us what we missed and he’s going to help us learn the game even more.”

Horford isn’t Boston’s best player. But make no mistake: He is the leader. In practices, timeouts, the locker room, wherever, his voice resonates.

“It’s incredible what he’s done all season,” Celtics Coach Ime Udoka said. “As I mentioned, came into training camp in extremely great shape, chip on his shoulder, prideful, wanted to come back to Boston. … He lays it all out there guarding bigs, smalls and everything in between. His leadership goes without saying.”

Winning the East title was hard enough, going through a No. 1 seed like Miami and having to win a Game 7 on the road made it even more difficult.

That told only part of the story.

Horford wasn’t himself in Game 6 on Friday night, when Boston had a chance to clinch the series on its home floor, and for understandable reasons. His grandfather died the day before, though family members urged Horford to keep playing.

“My grandfather was somebody that I was extremely close with, somebody that I really care for,” Horford said. “All week my mom, my family were just kind of telling me to just go out there and play. That’s something that he would have wanted me to do, to just continue on and really just try and stay focused and understand that he’s at peace now.”

There was grief. There was joy. The last few days have been quite the emotional pendulum for Horford.

But maybe it was fitting that the NBA Finals ticket came his way in Miami, given that he played his college ball at Florida and is a hero in his native Dominican Republic – where countless people have become Celtics fans again because of him.

“We’re here in Miami really close to the DR. Everybody is watching. The country was watching,” Horford said. “I know everybody was there. They were sending me pictures, they were ready for this, and we’re enjoying this time.”

Before long, though, he was already thinking ahead. The celebration in Miami had to end. A new challenge – the ultimate challenge for a basketball player, the one for an NBA title – awaits.

Finally.

“His energy, his demeanor, coming in every day, being a professional, taking care of his body, being a leader, I’m proud to be able to share this moment with a veteran, a mentor, a brother, a guy like Al Horford, man,” Brown said. “He’s been great all season, really my whole career. I’m happy to be able to share this moment with somebody like him.”