Instead of being history, the Celtics have a real chance to make history after dominating Heat in Game 5

Jayson Tatum and the Celtics stormed to a 61-44 lead at halftime of Game 5 at raucous TD Garden.Jim Davis/Globe Staff

It’s been building since they took back the night in the second half of Game 4 in Miami, and now it feels very real. The Boston Celtics are halfway home to a return to the NBA Finals.

One hundred and fifty NBA teams have tried, and 150 have failed, but your Celtics think they can become the first team in league history to recover from a 3-0 playoff deficit. The Celtics blew the roof off the Causeway Street gym Thursday, bolting to a 17-point first-quarter lead, pushing it to 24 in the fourth, and running the Heat out of town in with a wire-to-wire 110-97 Game 5 victory.

It was 48 minutes of blood and thunder basketball from the locals. Marcus Smart (23 points), Jayson Tatum (21), Derrick White (24) and Jaylen Brown (21) burned the Heat from international waters as Boston made 16-of-39 3-point attempts (41 percent) and dominated Miami with Lawrence Taylor defense.

“The Heat had a lot of focus on JT and JB, empowering me to shoot when I was open,’’ said White (6 of 8 on threes).

Game 6 is Saturday in Miami and Game 7 would be Memorial Day Monday night at the Garden. The Celtics’ level of confidence has to be high after what we saw in Game 5. The Celtics opened as 3-point favorites for Game 6.

The 2004 Curse-busting Red Sox are the only team in 123 Major League Baseball postseasons to recover from a 3-0 series deficit (at the expense of the hated Yankees, no less) and now their basketball cousins are a serious threat to make NBA history. It might behoove the Celtics to procure front-row seats for David Ortiz in Miami, and maybe summon Kevin Millar to the Hub for Monday.

“They let us get two, so don’t let us get another one,’’ said Brown, channeling his inner Millar.

There was a lot of confidence in Celtic Nation before Game 5. Fans seemed to have forgiven two home losses and the disgrace of Game 3′s 128-102 beatdown in Miami.

Green Teamers were buoyed by the memory of the Celtics’ comeback victory in Game 4 on the road and there was every expectation they could win again and recover from 0-3, like the Ortiz-Millar Red Sox.

The Garden crowd -- including Celtics owner Wyc Grousbeck -- was behind Derrick White and the rest of the team all night long.Barry Chin/Globe Staff

Celtics 34-year-old rookie coach Joe Mazzulla summed up his team’s plight in a dinner hour news conference saying, “Win or die.”

The Celtics burst out of the gate, bolting to a 16-point lead in the early minutes, canning 7 of 12 threes, forcing six Heat turnovers, and leading, 35-20, after one quarter. A 16-1 run highlighted the onslaught. Smart ignited the Garden crowd with a couple of corner threes and the Heat were reeling.

After a week of uncertain identity, the Celtics were once again the feisty front-runners we’ve come to know; all parts hustle and defense, with great confidence in their long-range game. There were plenty of second shots and 50-50 gathers. It was nearly perfect.

The surge carried into the second half and Boston took a 20-point lead on another three by Smart. They settled for 61-44 lead at intermission. White made 4 of 5 threes and had 14 points at halftime.

Boston pushed the lead to 24 (96-72) early in the fourth quarter.

So now it’s on.

Miami’s Jimmy Butler, who had a pedestrian 14 points in Game 5, warned, “We’re going to keep it very consistent, knowing that we’re going to win the next game.’’

The core of the Celtics believe otherwise.

Boston’s vaunted “Jays” — Tatum and Brown — have been playing together for six seasons and this is their fourth conference final. They made it to the NBA Finals last spring and led the Warriors, 2 games to 1 before dropping three straight. They had the second-best record (57 wins) in the NBA this season and beat the Atlanta Hawks in the first round in six games, and the Philadelphia 76ers in seven games in Round 2.

Then came the freefall against the Heat, losing a pair at the Garden, then getting trounced in Game 3 in Miami. Faced with disgrace in a sweep at the hands of a 44-win, eighth-seeded team, the Celtics rallied from a 9-point, third-quarter deficit and won Game 4 on the road, 116-99.

The crowd celebrates a first-quarter three from Jayson Tatum, who finished with 21 points.Jim Davis/Globe Staff

Now this.

They have bounced back from the edge of abject humiliation and are a legit threat to go where no NBA men have gone.

This is their time.