Billups’ three-point play pulled Detroit to 83-79 with 2:24 left, then the Pistons wasted a chance to get closer.

Tayshaun Prince grabbed a loose ball after a Boston miss and turned the ball over when James Posey surprised him from behind and snatched it away.

“He looked to his left, put the ball out and I just snatched it,” Posey said.

Pierce made two free throws on the possession, putting the Celtics up by six with 1½ minutes to go.

The Pistons failed on their 3-pointers down the stretch and couldn’t take advantage of Garnett and Pierce missing three free throws in the final 40 seconds.

The Pistons were eliminated at The Palace for the first time since Pierce helped Boston do it in the second round of the 2002 playoffs. Detroit had won its previous five games this postseason when coming off a loss.

With only one title and two NBA finals appearances during its impressive six-year run, the franchise will draw more comparisons to baseball’s Atlanta Braves.

The Celtics, meanwhile, validated their bold move of adding Garnett and Allen to join Pierce. Garnett and Pierce played key roles in the decisive fourth quarter, outscoring Detroit 20-13.

Boston point guard Rajon Rondo scored 11 points and Kendrick Perkins added seven points and seven rebounds.

Notes: Hamilton did not seem to be affected by a sore right elbow, which he injured late in the previous game. “My dad said to spit on it,” Hamilton said. “I guess that’s an old-school thing.” Did he follow the advice? “Yeah,” Hamilton said with a grin. ... Both teams were watching replays of Game 5 before Game 6 and were still complaining about the officiating. When Pierce was shown essentially tackling Billups in the previous game, he joked to teammates: “I got him down at the 2.” ... Faces in the crowd included Michigan football coach Rich Rodriguez, singers Kid Rock and Anita Baker along with Lions linebacker Ernie Sims. ... Detroit fell to 4-4 when trailing 3-2 in the playoffs, dating to the 2003 playoffs, when four of their current starters played key roles. ... The Celtics and Pistons met five times between 1985 and 1991, with Detroit winning three matchups.

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