Finally, a game in which the Celtics looked like the Celtics

Grant Williams, who is out of the doghouse, may have been the Celtics' second-best player in Game 4.Jim Davis/Globe Staff

That’s what this was supposed to look like. That’s what they were supposed to look like.

Teetering on the brink, the rumor mill churning, and the scalpels sharpened for the pending autopsy, the Celtics kept their season and their aspirations alive Tuesday night with a 116-99 victory over the host Miami Heat in Game 4 of the Eastern Conference finals.

The aesthetics weren’t always appealing, and victory wasn’t assured until the second half, when Jayson Tatum scored 25 of his 33 points and the Celtics overcame a 6-point halftime deficit. But for the first time since this series began, the Celtics resembled the well-connected, well-rounded team that had won 65 games this season (including eight in the playoffs) rather than the staggered victims of a stunning reversal of fortune in losing the first three games to the flawed but fearless Heat.

The Celtics extended the series — and at the very least now have Boston fans thinking hmmm as they reminisce about the 2004 Red Sox — by doing pretty much everything that made them an NBA title favorite.

Tatum started slowly, committing three turnovers in the first 7:50 (that’s a Russell Westbrook-like 18-turnover pace over a full game) and scoring just 5 points in the first quarter. But he was a Superstar, capital S, from there, hitting 14 of 22 shots overall (12 of 18 after the opening quarter), while also leading the Celtics in rebounds (11) and assists (7).

Tatum gets some grief, a fair percentage of it deserved, when he fails to put the Celtics on his back. But any notion that he habitually fails to come through in big moments demonstrates either a faulty memory or a desire to ignore reality to cling to a misguided take. Any suggestion of trading him is cause for immediate dismissal of all of that person’s basketball opinions infinitely.

Tatum was superb, and much of the deep supporting cast played familiar roles. Al Horford hit a three to start the game and drilled two more along the way in his best shooting game since he went 5 of 7 from three in Game 3 against the 76ers. Marcus Smart was mostly Good Marcus, hitting a couple of no-no-yes! 3-pointers and making mostly wise decisions with the basketball.

Who else? Derrick White (16 points) was essential in a 17-5 Celtics run in the second quarter, including a conventional 3-point play on a putback plus-one over Jimmy Butler and a savvy dish to a trailing Grant Williams for a three, which led to a Miami timeout.

Tatum & Celtics force Game 5 in Boston

Globe sports editor Matt Pepin talks about game 4 of the Eastern Conference Finals and whether the Celtics can come back from a 3-game deficit.

Speaking of Williams, he may have been the Celtics’ second-best player in Game 4, scoring 14 points, knocking down four 3-pointers (tied with Tatum for the team lead), and playing with energy and an edge all night. Whoever convinced coach Joe Mazzulla to free Williams from his prolonged and inexplicable stay in the doghouse deserves a bonus.

Jaylen Brown, usually the Celtics’ second star and scoring threat, is still struggling with his shooting — he was 1 for 5 from three in Game 4 and is 3 of 25 from deep in the series — but he deserves credit for playing a wiser game. Twice he found Robert Williams for point-blank buckets on nifty passes from the perimeter, the kind of playmaking that usually isn’t in his repertoire, and he hustled on defense and getting out on the break. I thought it was about as well as he could play on a night when his perimeter shot wasn’t cooperating.

The Celtics also hit 18 of 45 3-point attempts, a math game Mazzulla always prioritizes. Save for Sixth Man of the Year Malcolm Brogdon’s disjointed performance, this victory just looked familiar, and the Celtics looked like the team we were expecting to see from the beginning.

The Heat’s role players, who looked like a Splash Brothers tribute band in the first three games, cooled off considerably from the perimeter. Gabe Vincent, Caleb Martin, Duncan Robinson, Kyle Lowry, and Max Strus combined to shoot 5 of 23 from three. More regression to the mean is possible. The Celtics also have a depth advantage, particularly if Vincent’s late-game ankle injury hinders him in Game 5.

The energy, as they say, may have shifted. And if you want to believe other mystical forces could be at play, I’m not going to try to dissuade you. There are at least inklings and hints and vague suggestions of the “don’t let us win tonight” 2004 Red Sox in this series. Tatum will have to play the role of David Ortiz, of course. But who would be Dave Roberts? Maybe White, a similarly unassuming sort with a knack for coming up with a steal.

Someone around here should write a thank-you note to the Heat for putting Alex Rodriguez and Derek Jeter courtside in Game 4. If Keith Foulke and Mariano Rivera are sitting next to each other Thursday night in Boston, I might believe something is up here that is beyond our control but not our imaginations.

Even with this twinkle of renewed hope, it’s difficult to avoid wondering how this series would look right now had the Celtics not blown the first two games at TD Garden. But there are no do-overs, and there is no point in looking back now. The next game could be the last game, and surviving that is all that matters.

The Celtics survived, and thrived in the most important moments, Tuesday night. They are alive to play another day. We won’t get ahead of ourselves, but there are legitimate reasons for the small but real hope that they might just be able to win one more time, and one more time, and one more time again.