There was a time when the Boston Celtics’ season seemed in danger of crumbling into a pile of fine dust. They had a losing record in late January. They were scuffling through a series of injuries. There were questions about whether Jayson Tatum could coexist with Jaylen Brown — was it time for the team to consider trading Brown? — along with inevitable critiques of Ime Udoka in his first season as coach.

It is familiar history at this late stage of the season, but worth reiterating, especially now. Why? Because on Friday night, in the wake of a late-game meltdown earlier in the week, the Celtics were facing elimination in Milwaukee. Outside of their cocoon, as they braced themselves for Game 6, the questions swirled: Had they blown their chance? Could they somehow find the resolve to extend their Eastern Conference semifinal series with the Bucks?

The Celtics, though, seem to embrace adversity. Perhaps they are conditioned to play at their best when everyone else thinks they are finished, a sandcastle about to be swept to sea. Down? Out? Their sandcastle is apparently reinforced with steel beams, and they proved as much with their 108-95 win.

“This was a big moment for all of us,” Tatum said just minutes after assembling one of the finer individual performances of the N.B.A. postseason. “I think we showed a lot of toughness and growth.”

There was no doubt about that after Tatum finished with 46 points and 9 rebounds to help even the series at three games apiece. In the process, he somehow overshadowed Giannis Antetokounmpo, who tried to drag the Bucks across the finish line with 44 points, 20 rebounds and 6 assists. It was a series that deserved a seventh game, and the Celtics delivered. Game 7 is on Sunday afternoon in Boston.

“I believe in everyone in that locker room,” Tatum said. “We have what it takes.”

The Miami Heat, who ousted the Philadelphia 76ers from the postseason on Thursday, are awaiting the winner in the Eastern Conference finals, with the opening game of that series set for Tuesday. The Heat must have been delighted to see the Celtics extend their series with the Bucks: Now those teams have time to bludgeon each other some more.

“You got two juggernauts going at it,” the Celtics’ Marcus Smart said. “We’re beating each other up.”

The Celtics are grateful to be in this position after collapsing in the fourth quarter of Game 5 on Wednesday. That game could have haunted them after they blew a 14-point lead. Smart, in particular, was furious with himself for making a couple of late-game gaffes. He recalled going straight to the team’s practice facility after the game, and then tossing and turning through two sleepless nights ahead of Game 6.

“I feel like I let my team down,” he said.

The good news, Udoka said, was that the Celtics had played well in Game 5 — until they stopped playing well. The winning components were there. And they were on display again in Game 6, this time for a full 48 minutes.

Smart was terrific, finishing with 21 points and 7 assists without a turnover. Brown scored 22 points. And consider the contributions of Derrick White, a former Division II player and trade deadline acquisition who was all over the place in the final three minutes of the first half. He followed up a 3-pointer with a short jumper. He drew a charging foul on Antetokounmpo. And then he made two free throws, lifting the Celtics to a 10-point lead at halftime.

But the reality was that Smart, Brown and White were a part of the supporting cast. The stage belonged to Tatum.

“He went into another mode,” Smart said. “We seen it in his eyes.”

From the start of the playoffs, when he christened the Celtics’ first-round series with the Nets with a game-winning layup, Tatum has gone about his business of elevating his stature as one of the league’s most ferociously skilled players.

No, he has not been immune from the occasional clunker. In a narrow loss to Milwaukee in Game 3, he shot 4 of 19 from the field and missed all six of his 3-point attempts. But in the three games since, he has averaged 36.7 points, 9.3 rebounds and 4.3 assists while shooting 47 percent from the field.

On Friday, Tatum played a brilliant all-around game. He did more than score. Coming out of a timeout in the third quarter, he stripped the Bucks’ Bobby Portis in the post, leading to a layup for Brown and a 17-point lead.

Tatum also was able to counter everything that Antetokounmpo could throw at the Celtics, which was a lot. The Bucks were threatening in the fourth quarter when Antetokounmpo sank a 3-pointer. Tatum proceeded to score the Celtics’ next 10 points, a flurry capped by a deep 3-pointer over the top of the Bucks’ Pat Connaughton.

“Obviously, I know when I have it going,” Tatum said. “You feel that rhythm.”

No one is counting out Milwaukee, of course. The Bucks are the defending champions, and Antetokounmpo is capable of intergalactic feats. But without the floor-spacing presence of Khris Middleton, an All-Star forward who has been sidelined with a sprained left knee, Antetokounmpo has had to do even more Antetokounmpo things than usual.

He clearly needs more help from his teammates on Sunday, especially against the likes of Tatum, a star in his own right.

Now, after a season of surviving and growing, the Celtics see nothing but opportunity ahead of them.

“We still have a chance,” Udoka said, “to make it a better story.”