As the New Big Three celebrated their first NBA championship Tuesday night and into the wee hours of Wednesday, I thought back to the May night in 1981 when the original Big Three celebrated their first NBA title.

What a difference.

Larry Bird, Kevin McHale and Robert Parish celebrated in a cramped dressing room in The Summit, home of the Houston Rockets, whom they had just dispatched in six games. The champion Celtics were soaked with some brand of cheap sparkling wine, and I think Bird and McHale were waving big cigars, courtesy of Red Auerbach, who had one of his own.

Coach Bill Fitch, who had taken one of the worst teams in the NBA in 1978 and ’79 to the Eastern Conference finals in 1980, praised Parish, whom Cedric Maxwell had nicknamed “Chief” that season after the stoic character in One Flew Over the Cuckoo’s Nest, as long as anybody would listen.

Maxwell, the best player on those bad teams in ’78 and ’79, was the NBA Finals MVP.

It was quite a scene, and the partying lasted through the night. The next morning, as the Celtics staggered to the hotel lobby for their commercial flight back to Boston — there were no team charters in those days — McHale looked as green as his road uniform. Too many toasts and too many cigars, no doubt.

Those memories came back as I watched the lovefest at TD Banknorth Garden on Tuesday night. Paul Pierce, Kevin Garnett and Ray Allen savoring the cheers of 18,000 adoring fans and hugging each other as the final, meaningless minutes of the 131-92 rout of the Lakers played out.

The New Big Three, bouncing on their toes, as excited as 5-year-olds on Christmas morning. Confetti blowing from the parquet to the rafters. Later, in the Celtics’ dressing room, wives and children shared the joy as the new champions sprayed each other with bubbly.

They deserved every last cheer, every last hug, every last drop from the bottle, I thought. Not that the Big Three in 1981 didn’t. But the situation was different then. The Big Three had most of their careers in front of them. Parish, who had played for Golden State for four years, was the old man of the group, and he was only 26. Bird, in his second year in the league, was 24. McHale, a rookie, was 23.

The Big Three had yet to hit their prime, as basketball professionals or as young men, and given their age and their success — Bird won 123 games and a championship in his first two seasons — they had every reason to believe they would return to the winner’s circle.

And they did, but not without growing pains. Philadelphia was the better team in 1982, and Milwaukee swept the Eastern Conference semifinals in 1983, leading to Fitch’s ouster. But with K.C. Jones on the bench and newly arrived Dennis Johnson at the point, the Celtics began their remarkable run of four consecutive NBA Finals and championships in 1984 and 1986.

The New Big Three reached the top under different circumstances. They were veterans of a decade or more, and Danny Ainge assembled them to win in 2008, not next year or the year after, although that may be the case if they remain healthy. Pierce, Garnett and Allen had 32 years of NBA experience at the start of this season.

They had done everything in the game except win a championship. They had earned Hall of Fame credentials but no ring. Garnett had been to the playoffs eight times with the Timberwolves but never beyond the first round. Pierce and Allen had been four times each but had never reached the NBA Finals.

The New Big Three understood that time was not on their side. Garnett was 31 at the start of the season and turned 32 last month. Allen was 32 and Pierce 30. They also understood from the beginning that each of them would have to sacrifice part of their individual games for the sake of the team.

The New Big Three brought a maturity to the Celtics that the Big Three had to develop. It showed late in the playoffs, when Pierce spoke about the need for his teammates to appreciate their position and be aware that a return trip was not guaranteed.

That maturity also showed after the Celtics won. There was no gloating, no belittling the Lakers in the wake of a 39-point drubbing. Only heartfelt relief that they had accomplished their goal and reached the top of the basketball world.

Pierce, a career Celtic, could look up at all of those banners hanging from the rafters and realize that he had finally earned his place among the Celtics’ greats. That Bill Russell, John Havlicek, Tom Heinsohn and Jo Jo White were there Tuesday night to witness his final ascent made the experience all the more fulfilling. Garnett and Allen could finally pronounce their All-Star careers complete.

Russell had promised Garnett one of his 11 championship rings if KG fell short in his quest, but the generous offer wasn’t necessary. As the championship celebration began on the parquet, the two giants embraced, and Garnett wailed, “I got mine! I got mine!”

mszostak@projo.com