Is it physically possible to feel exhausted and exhilarated all at once? Miami Heat fans can tell you this morning. They’ll be smiling when they do, guaranteed.

The Heat dramatically rallied and fought and earned every bit of one of the greatest victories in this club’s 24-year history here Saturday night — in simply the biggest Game 7 playoff test this franchise had ever faced.

Nerves and emotions and scoreboard leads caromed and swung, leaving players and witnesses alike drained on surely one of the great nights in South Florida sports.

Exhale, but quickly. Rest up, but not for long.

Because now the fun starts.

Ain’t it great!?

Miami’s season-saving fourth quarter beat the Boston Celtics, 101-88, Saturday in the finale of the NBA’s Eastern Conference finals, in a downtown bayside arena as full and sonic-loud as it ever has been.

Now the Heat advances for the second year in a row to the NBA Finals, vs. the Oklahoma City Thunder beginning there Tuesday night, aiming for the championship trophy Miami narrowly missed last year.

It all happened — this essential victory earning this title chance — simply because of this:

Miami’s Big 3 have never been bigger.

LeBron James, Dwyane Wade and Chris Bosh, all of them, have never in their two seasons together collectively produced like this in an elimination game, where everything is at stake, where clutch and choke separate themselves.

The three of them combined to score the first 26 Heat points in the fourth quarter, when Miami puts its fingers on Celtic necks and began to squeeze as the white-clad crowd stood and roared.

After scoring a mammoth 45 points in the previous game, James assured, “I won’t regret Game 7.”

Consider it a promise kept.

James would score 31 points, adding 12 rebounds. Wade would add 23, and drive that late rally. And Bosh, in only his third game back from an abdominal strain, scored 19 points on 8-for-10 shooting, including three three-point baskets, a career first for him.

As good as James and Wade were, Bosh might have been the player of the night.

“We missed him. Happy to have him back at the right time!” James said afterward. “We wanted to give our fans a big win. Now we look forward to the next challenge.”

It was James who most carried the Heat into the Finals, though, and Wade acknowledge that afterward in a sort of passing of the baton that was quite extraordinary, considered this had been “Wade’s team” for so long.

“He’s emerged as the leader of this team, and we follow him,” Wade said of James. “He’s going to continue to be great.”

The Heat accepted the Eastern Conference trophy in an on-court ceremony afterward, but it isn’t the hardware this team requires. Or needs.

This was the Heat’s first Game 7 at home since 2005, an event as much as a game, and the stakes showed in the unlikeliest sight of all in fashionably late South Florida: Every seat filled before tipoff.

Courtside seats in the jammed building sold for as much as $10,000, according to ticket brokerage StubHub, but a single ticket remained available as the game began, of course.

It was a ticket to the NBA Finals. You couldn’t buy it, no matter how much money you spent. One team would win it.

Miami needed it.

No team more than the Heat has faced pressure to win not only a championship, but many of them.

Two of our other big teams will be starring in summer reality series — the Marlins on Showtime’s The Franchise and the Dolphins on HBO’s Hard Knocks — but it this Heat team that has starred in a national soap opera for two years now, chased all the while by a searing spotlight.

Much of the pressure has been self-imposed.

It was James, after the Big 3 came together, who promised multiple titles, shouting to Heat fans, “Not two, three, not four…” — and not stopping until he got to seven championships.

That has to start with one.

Saturday night gave that a chance to happen.