When the Celtics began to reconstruct their roster, the occasional returns of former stars were a welcome distraction, a chance to remember when the franchise was flourishing. And so a game like Wednesday’s, with Doc Rivers and Paul Pierce coming back to TD Garden, would usually be a perfect chance to look back.

But with these Celtics, there is no longer a need for any sideshow. They are now compelling enough on their own, and so this game was really a chance to test themselves against an elite team.

It was a chance to find out how they would rebound from a disheartening loss in Milwaukee one night earlier. A chance to find out how they can close out a team with Jae Crowder and Marcus Smart having fouled out, and Kelly Olynyk in a hospital getting X-rays on an injured shoulder. A chance to see if they were resilient enough to claw back from a 5-point hole in the final minute of regulation and a 6-point deficit early in overtime.

“This team’s mentality is no matter what the situation is, we are not going to give up,’’ point guard Isaiah Thomas said. “We’re going to keep fighting until there is no time on the clock. That’s what makes this team special.’’

When the final buzzer sounded, the Celtics had snagged a 139-134 overtime win over the Clippers in front of a raucous Garden crowd. Their celebration was not flashy, but as they embraced one another at game’s end, it was clear this win had resonated.

“The resiliency that we showed and the character we showed tonight, it speaks volumes of everybody from top to bottom,’’ Crowder said. “The coaches stay calm and the players stay calm and stay the course of the game.’’

With 45.6 seconds left in regulation, Thomas converted a floater to pull the Celtics within 122-120. Chris Paul missed a 3-pointer with 24 seconds left but Crowder was whistled for fouling DeAndre Jordan on the rebound.

Jordan missed both free throws, however, and at the other end Thomas probed the defense before swishing a difficult 15-foot fadeaway jump shot with 5.8 seconds left, tying the score at 122 and ultimately forcing overtime.

Paul and Thomas, a pair of All-Stars, were locked in a dazzling duel throughout this game. Thomas finished with 36 points and 11 assists and Paul countered with 35 points and 13 assists.

“I’m all for challenges,’’ Thomas said, “and I’m all for going against anybody.’’

The Clippers started overtime quickly, with J.J. Redick getting fouled as he made a 3-pointer and then fouled on another 3-pointer. He missed one of those free throws, but less than a minute into the extra session the Clippers suddenly had a 128-122 lead.

Los Angeles struggled from the foul line in the extra session, though, as normally reliable shooters such as Redick, Jamal Crawford, and Paul combined to miss four free throws.

With 2:25 left, Celtics forward Jared Sullinger, a 26 percent 3-point shooter, drained a three from the right arc to pull his team within 131-130. Evan Turner then made consecutive baskets, the second a 3-point play that gave the Celtics a 135-132 lead.

After a layup by Paul pulled the Clippers within 1, Turner drilled another fadeaway to make it 137-134.

“I had the confidence I could make big shots,’’ Turner said. “I felt great; I was just waiting for it.’’

At the other end, Pierce’s return would provide no fairy tale, as he missed a 3-pointer from the left arc. The Clippers had a final chance, but Crawford’s 3-pointer with 10 seconds left caromed off the backboard and curled around the rim before rolling out. Jonas Jerebko was fouled after the rebound and made both shots, and the Celtics sealed their wild win and entered the All-Star break with momentum.

“Just keep fighting,’’ Thomas said. “That’s what this team is about. Never give up. Just continue to fight, no matter what the circumstances are. At a point in time in that game, our backs were against the wall, it seemed like the game was over, but we just kept at it.’’

Sullinger finished with 21 points, 11 rebounds, and 7 assists.

The Clippers held a 41-33 lead early in the second quarter, but the Celtics clawed back against Los Angeles’s second unit. They scored 9 consecutive points, and a 3-pointer from the top of the key by Avery Bradley capped a 22-8 burst that gave the Celtics a 55-49 lead.

With 7:47 remaining in the third quarter the Celtics took their largest lead, 81-68, on a basket by Bradley. But the Clippers ultimately surged back behind Paul.

The All-Star point guard hit a 3-pointer before the third quarter buzzer to make it 98-91, and the good feeling from that shot carried into the fourth. Over a stretch of 2:23, Paul made a floater and drained a pair of 3-pointers, the second tying the score at 103.

With 6:34 left, a Crawford 3-pointer gave the Clippers a 109-107 lead, their first since 47-46. The Clippers extended their advantage to 117-111 with three minutes left. With 2:13 remaining, a jumper by Sullinger pulled the Celtics within 118-115.

With the Clippers leading, 120-115, the Celtics chased down a pair of rebounds after missed 3-pointers and Thomas then attacked the basket and was fouled as he made a layup. Thomas missed the ensuing free throw but Smart grabbed the rebound and was fouled.

Smart made the first foul shot and missed the second, and gave chase for the rebound once more. But this time he was whistled for his sixth foul when he made contact with Redick. Redick’s two free throws made it 122-118 with 53.1 seconds left. But the Celtics knew they were not finished.

“We see it’s happening,’’ Crowder said. “It just takes all five guys on the court just staying in the moment, not getting too down on ourselves and staying the course of the game.’’

Adam Himmelsbach can be reached at adam.himmelsbach@globe.com. Follow him on Twitter @adamhimmelsbach.