BOSTON — The magic number is one for the Boston Celtics to clinch the top spot in the Eastern Conference.

Boston players were in their locker room after a 114-105 victory over the Brooklyn Nets on Monday night when the Cleveland Cavaliers, playing without the resting LeBron James and Kyrie Irving, lost in overtime at Miami.

Clapping could be heard from the trainer’s room, where players were tuned in.

“Yeah, we were watching a little bit of it,” Celtics guard Marcus Smart said. “We’re aware of what’s going on, and hopefully we can get the one seed.”

The Celtics (52-29) clinched their first Atlantic Division title since 2011-12 while grabbing a one-game lead in the East with one game remaining. They need a home win over the Milwaukee Bucks on Wednesday or a home loss by Cleveland (51-30) to the Toronto Raptors the same night to clinch the top seed.

The division title?

“I don’t even know what divisions are for anymore … I guess it means something,” Celtics coach Brad Stevens said. “It’s not something we’ve talked about and I guess in Boston you only talk about one goal, right? So everything else is leading up to that.”

The victory completed a four-game sweep of the season series with the Nets, who will provide Boston with one of the top picks in the draft lottery thanks to the Kevin Garnett-Paul Pierce trade that keeps on giving.

Isaiah Thomas scored 27 points, Al Horford had 19, and the pair combined for the final 15 Boston points over the last 4:41. Horford grabbed eight rebounds and added four assists.

Boston’s Avery Bradley scored 18 points, Smart had 13 points and six assists, Jae Crowder 11 points, eight rebounds and six assists, and Kelly Olynyk 11 points and six boards.

“Trying to finish the season with the No. 1 seed, that means a lot to me, personally, so hopefully we can get that,” Thomas said. “We’ve been through ups and downs, we’ve been through a lot of injuries this year — haven’t been healthy for the most part. We just kept going.”

The Celtics built a 27-point lead in the third quarter, but a 37-point quarter and then another charge in the fourth got the Nets, who scored 40 in the first half, to within six in the fourth. Runs of 12-0 and 9-0 got them there.

“We have to play better than we have the last two games with the lead,” Stevens said.

Despite the loss, Brook Lopez scored 25 points and became the Nets’ all-time scoring leader, passing Buck Williams.

“It’s a great honor, obviously a lot of amazing players have played here,” said Lopez, who finished the game with 10,434 career points. “I’m just proud to have my name up there with those guys.”

Jeremy Lin, a former Harvard star playing on Chinese Heritage Night at TD Garden, scored 26 points and grabbed a career-high 12 rebounds, and Rondae Hollis-Jefferson scored a career-high 17 points and had 11 rebounds.

Lin was told about Lopez’s record.

“That happened tonight? Oh, wow,” he said. “I literally had no idea what he needed. I heard people mention it might happen at the end of the season. After that, I kind of forgot about it. That’s awesome. I’m really happy for him. Huge congratulations for him to do what he’s done. If I could describe Brook in one word, it would be consistency.”

The Nets, who have been playing better and refused to quit in this game, lost for the second time in six games.

The Celtics improved to 24-0 when leading after three quarters at home.

As far as the division title, Smart said, “It means a lot to us as a team. It shows that we’re starting to play the right way. This is going to help us get closer to our goals and we just need to finish out strong and prepare for the playoffs.”

NOTES: Celtics coach Brad Stevens, pregame, on the importance of securing the top seed in the conference: “The most important thing is tonight’s game. That’s the way I’m looking at it. Whatever seed we get, we get — and that’ll be a result of an 82-game schedule, not the result of one or two games.” … The Nets were missing Gs Sean Kilpatrick (hamstring) and Joe Harris (shoulder) and F Quincy Acy (ankle). All three will also miss Wednesday’s night’s season finale at Chicago. … Nets coach Kenny Atkinson on Boston G Isaiah Thomas: “Just thinking about his evolution since he got here, how much he’s improved and how he fits into the system, he’s a scouting nightmare, trying to figure out how to get him under control. He’s the head of the snake. Just really a credit to the Celtics and credit to him. He just keeps getting better.” … Thomas extended his club record with a 3-pointer in his NBA-high 56th straight game.