They had to after some lean seasons, but the transformation nonetheless has been instant and remarkable. There seemingly has been no feeling-out period required for the team's so-called Big Three.
Boston started 8-0, its fourth-best start in franchise history.
Dwyane Wade of the Miami Heat said he is not surprised. For one, the Heat did something similar when it traded for Shaquille O'Neal and later added Jason Williams and Antoine Walker, a blending of stars that eventually led to the Heat's first title.
More than that, Wade said, he figured that Garnett, a 10-time All-Star and 2004 Most Valuable Player with the Minnesota Timberwolves, would make it work.
"You've got to look at the personnel and understand that K.G. is a very unselfish player, and he is the main guy in the offense," Wade said. "Ray Allen is an unbelievable shooter. Paul is Paul. He's the truth.
"They've got a great combination of guys. It's kind of amazing how it's all been put together."
The Celtics' changes weren't as risky as those the Heat made two seasons ago. Boston hadn't made the playoffs in five years. The Heat was coming off an Eastern Conference finals appearance when Pat Riley traded two starters for Williams, Walker and James Posey.
Celtics general manager Danny Ainge, feeling the pressure from the losing, quickly shifted out of youth mode. He traded the fifth pick in the draft to the Seattle SuperSonics for Allen and then acquired Garnett from Minnesota in July.
The Celtics have gotten the expected scoring boost from two career 20-point scorers. They also have shown strength on defense, leading the league by allowing 88.9 points a game.
"We never worry about our offense as much as we worry about our defense," Garnett said recently. "We know at the end of the day that's how we can win games, with defense."
The Big Three wouldn't be enough for Boston. The trades left it with little depth, so Ainge filled holes with low-budget free agents Posey, Eddie House and Scot Pollard. Injuries have slowed Pollard, but Posey and House have fit in nicely as Boston's top two reserves.
"We needed shooting, we needed experience, we needed defense, we needed size," Ainge said. "We got Posey and Pollard and Eddie. That covers them all right there."
Posey joined the Celtics after a disappointing summer on the free-agent market. He has emerged as a leader in Boston, where Ainge says Posey is "our Tedy Bruschi, our Jason Varitek," referring to role players with the New England Patriots and Boston Red Sox, respectively.
There are reasons to doubt the Celtics, despite the fast start.
Allen, 32, and Garnett, 31, have 23 combined years in the league, and the Celtics' depth isn't terrible, but a major injury to those two or Pierce could wreck the season. Close losses at Orlando and Cleveland showed that Boston is sorting out late-game roles.
"Us closing out games, I think that is where we have to mature as a team," Allen said. "We are new to each other. Closing out games is important to us because that is what it is going to take in the playoffs."
None of the Big Three has had much success in the playoffs recently, another reason that the Celtics' moves were met with skepticism. Wade said he viewed that as a reason to believe the Celtics would come together quickly.
"You are hungry," Wade said. "You want to prove everybody wrong or everybody right. That is what they are doing, playing exceptional basketball because everybody is hungry."
Michael Cunningham writes for the South Florida Sun-Sentinel.