‘We didn’t want to go out like that:’ The Celtics still face a battle, but Game 4 showed there’s reason to believe

Celtics center Robert Williams howled after throwing down a ferocious dunk in the fourth quarter.Jim Davis/Globe Staff

MIAMI — Celtics center Robert Williams was sitting down and surrounded by a crush of reporters after the team’s morning shootaround Tuesday. As 6-foot-9-inch Al Horford walked past him, he had to briefly stand on his tiptoes to see who was on the other side of the scrum.

Once he noticed it was his frontcourt mate, he smiled and nodded as he called out to Williams.

“We’ve got it tonight, Rob!” Horford said. “We’ve got it tonight!”

Later, Marcus Smart and Jaylen Brown took their turns in front of the cameras and microphones, and emanated similar confidence despite the 3-0 deficit their team faced in the Eastern Conference finals against the Heat. A deficit no NBA team has ever fully overcome, despite having 150 tries to do it.

“I feel very good about tonight,” Smart said. “Don’t let us get one. Just don’t let us get one.”

Now, the Celtics have their one. In Game 4 on Tuesday night, they used an 18-0 run to roar back from a 9-point, second-half deficit and keep their season alive with a 116-99 win, Miami’s first home loss in these playoffs. Game 5 will be played at TD Garden on Thursday night.

Tuesday’s result was the kind that most expected when the Celtics entered this series as massive favorites against the eighth-seeded Heat. And while the challenge in front of the Celtics remains substantial, the thoroughness of this win, the general belief that they are the superior team, and the fact that two of the final three games of this series would be played at TD Garden makes their chances feel like more than a pipe dream.

“Now, we’ve just got to go win another one,” Smart said after the win. “That’s all that matters . . . We understand the odds are stacked against us, but we’re a team that believes in us no matter what, and we’ve just got to keep going.”

The Celtics were walloped by 26 points in Game 3 on Sunday night. The manner in which they lost combined with the daunting series deficit they faced certainly made the end quite visible. Forward Jaylen Brown said the Celtics gathered as a team Monday night and talked about the long path in front of them. They came to the agreement then that they were not done.

“Definitely with our backs against the wall,” he said, “we didn’t want to go out like that.”

In Game 4, the Celtics got back to doing what had made them so dangerous as they emerged as NBA title favorites for most of this season. They efficiently and accurately sprayed 3-pointers after making an extra pass to get open ones. One game after coach Joe Mazzulla said they seemed to have lost their defensive identity, they bothered the Heat’s shooters who had been outperforming them during this series. And when they faced deficits, they did not unravel; they kept their poise and punched back.

Jayson Tatum, whose play has been uneven during this series, shook off a lukewarm first half and was dominant in the second, when he erupted for 25 of his game-high 33 points. He added 11 rebounds and seven assists.

“I think we just had to settle down a little bit,” Tatum said. “We saw a couple go in and started to play free.”

The Celtics made 19 of 45 3-pointers, finishing above the 40 percent mark that has generally been their bellwether for success this season. Horford snapped out of his shooting slump to hit 3 of 6, and Grant Williams, who has stormed back into the rotation after long stretches of watching, came off the bench and hit 4 of 6.

Tatum hit for 33 points in Tuesday's win.Jim Davis/Globe Staff

The Heat, meanwhile, connected on just 8 of 32 attempts, as role players such as Max Strus, Duncan Robinson, and Gabe Vincent who had improbably put Miami on their shoulders suddenly appeared to feel the weight.

Yes, Jimmy Butler still scored 29 points. But silencing the secondary pieces was what truly mattered. The Celtics forced 16 turnovers.

“We brought the pressure to them,” Smart said. “We weren’t playing off our back foot, like we have been in this series. We were the aggressor on both ends.”

Of course, plenty of looming shadows remain. The Celtics have been a .500 team at home during these playoffs, are 0-2 there against the Heat in this series already, and NBA teams are 0-150 all time when trailing, 3-0, in a best-of-seven. But this is not over. Not yet.

“We didn’t want that [Game 3 loss] to define us, define the season,” Tatum said. “We’ve still got a long, uphill battle to go. But tonight was a good start.”

A play early in the third quarter seemed to epitomize this series for Boston. Butler missed a wide-open layup, and the ball ended up in the hands of Strus, whose 3-pointer was blocked by Tatum. But he got the ball back and hit his second try, giving the Heat a 61-52 lead, their largest.

The Celtics did not score on its next two possessions, and on the third, Tatum appeared to be stripped cleanly by Kevin Love. But a foul was called, and Tatum then drilled two 3-pointers in a 23-second span, igniting the game-defining 18-0 run.

The Heat made a push at the start of the fourth quarter, pulling within 88-83 during the Celtics’ three-minute scoring drought.

But Mazzulla called time out, Tatum reentered the game, and the Celtics seized control of the win with a 12-0 burst.