Boston, which locked up with Detroit many times in the 1980s, will now rekindle another classic series in the NBA finals against the Los Angeles Lakers.
"It's kind of surreal," Garnett said.
The Celtics are in the NBA finals for the first since losing to the Lakers in 1987, the third meeting in a four-year span.
The Pistons were eliminated on their home court for the first time during a six-year run that included a trip to the conference finals each year and the 2004 title.
Boston entered the series without a road win in the postseason, then beat Detroit on its home court twice to win the grueling series.
After playing two Game 7s, the Celtics will get a needed break before hosting Kobe Bryant and the Lakers on Thursday night.
"We're emotionally drained," Garnett said.
Chauncey Billups scored a playoff-high 29 points and Richard Hamilton had 21, but the rest of their teammates had lackluster efforts - especially Rasheed Wallace.
At one point Billups had 21 points, matching the total for the rest of the team.
Wallace scored just four points on 2-of-12 shooting and had three turnovers in what might've been his last game as a Piston and could've been Flip Saunders' last as Detroit's coach. President of basketball operations Joe Dumars will likely make some sort of changes on the bench, the court or both.
"I'm sure that's something Joe and I will sit down and evaluate," Saunders said.
After it was 58-all, Detroit closed the third quarter with a 10-2 run and took its first lead since midway through the opening quarter.
Just when it seemed the Pistons might be in control with a 70-60 lead early in the fourth, the Celtics scored nine points in less than 2 minutes and went on a 19-4 run that put them ahead 79-74.
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.
Pierce made two free throws on the possession, putting the Celtics up by six with 1½ minutes to go.
"It was the best fourth quarter we played all playoff long," Pierce said.
The Pistons failed on their 3-pointers down the stretch and couldn't take advantage of Garnett missing two free throws with 36 seconds left.
The Pistons were eliminated at home 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.
Detroit lost Game 6 of the conference finals for the third straight year and 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 Pierce to form a Big Three. They played key roles in the decisive fourth quarter, helping Boston outscore Detroit 29-13.
Boston point guard Rajon Rondo scored 11 points and Kendrick Perkins added seven points and seven rebounds.
Unlike early games in the series, neither team jumped out to a big lead in the opening minutes.
Boston led 24-21 after five lead changes - the last coming at the 6:12 mark - and a tie in the first quarter and a negated shot.
Pistons rookie Rodney Stuckey made a jumper late in the quarter, but it was waved off after a video review showed the ball in his hand when the shot clock expired.
Allen and Hamilton, in a matchup of Connecticut greats, had 10 points apiece in the first quarter to lead both teams.
After the Celtics went ahead by seven, Billups made a 3-pointer and later a free throw to pull Detroit within a point.
Garnett then went to the bench with three fouls and 3:11 left in the first half, and seldom-used reserve Leon Powe replaced him and matched the superstar's point total of four points to help Boston lead 40-37 at halftime.
Garnett opened the game by making his first two shots, then missed his final eight attempts in the first half.
Both teams had two starters making shots and three putting up bricks.
Billups and Hamilton were a combined 11-of-19, while the other three starters were 1-for-12. Wallace and Prince missed all five of their shots.
Allen and Pierce combined to go 9-of-15. The rest of the starters were 5-for-21.
Garnett and Prince both ended their skids by making jumpers early in the second half.
Prince scored nine points in the third to help Detroit score 31 in the quarter after being held to just 37 in the first half.
Antonio McDyess made two free throws with 3 minutes left in the third quarter to put Detroit ahead as part of a 22-6 run that gave it a 10-point cushion early in the fourth.
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.