BOSTON - Not even a week of rest could prepare the Detroit Pistons for the hottest home team in the NBA.

Kevin Garnett had 26 points and nine rebounds and Paul Pierce scored 22 points Tuesday night to give Boston an 88-79 victory over the Pistons in Game 1 of the Eastern Conference finals, the Celtics’ 15th straight home win.

Despite having just one day off after an epic Game 7 that eliminated LeBron James and the Cleveland Cavaliers from the conference semifinals, Boston scored the first eight points against a Detroit team that waited six days for the series to start.

“Rest is not an option,” Garnett said. “So we don’t even think about that.”

Kendrick Perkins had 10 rebounds for Boston and Rajon Rondo scored seven of his 11 points in the fourth quarter, hitting a 3-pointer with 1:47 left in the game after the Pistons cut the deficit to 83-75. Rondo also had seven assists and five steals while outplaying Chauncey Billups, the MVP of the 2004 NBA finals, in his return from a right hamstring injury.

“I believe in him. I play him. I’m going to keep playing him,” Celtics coach Doc Rivers said of his point guard. “I told him before the game, ’Stop worrying about them. Make them worry about you, too. You’re a hell of a basketball player.”’

The Celtics earned home court through the playoffs with a league-best 66-16 regular season record and rode that advantage to seven-game victories in series against Atlanta and Cleveland. On Tuesday they improved to 9-0 at home in the playoffs, but they’re 0-6 on the road.

“They haven’t lost a game; they should be confident,” said Billups, who missed the last 2½ games of the Orlando series. “They have been very good here at home. We are usually a really good team; we didn’t have a good game today, but we look forward to Thursday.”

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While Detroit rested, the Celtics have been playing every other day. Boston’s 15 games is the most of any team still in the postseason.

“You have to figure, doing this every other day, you just get used to the same routine of coming out, being out this late, playing basketball,” Celtics guard Ray Allen said. “I think when you get that break in between, you have to build yourself back up into it.”

Billups scored nine points with two assists, two steals and two turnovers in his first game since May 7. Tayshaun Prince scored 16 points and Antonio McDyess added 14 points and 11 rebounds for the Pistons, who have one more chance to win in Boston on Thursday night before returning to Detroit for Games 3 and 4.

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“This was the perfect game for them to come in and try to steal one,” said Pierce, who scored 41 in the finale against Cleveland. “And we were aware of that.”

But Detroit looked rusty early, missing its first five shots while allowing Boston to take an 8-0 lead on Allen’s drive with 8:36 left in the first.

“We just didn’t seem to be in a good flow, it might have had something to do with (the layoff). We were just a step slow,” Pistons coach Flip Saunders said. “We didn’t get into the flow.”

Billups hit a second-chance 3-pointer to end the drought and make it 8-3. But he did not make another field goal — he had four points and no assists in the first half — until there was 4:47 left in the game.

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The Pistons quickly erased the first-quarter lead, even going ahead 13-12. But they trailed 41-40 at halftime and scored just 17 points in the third quarter, 10 from Richard Hamilton, while the Celtics took a 69-57 lead on Eddie House’s 3-pointer with 2 seconds left.

Notes: Allen, who shot only 33 percent in the second-round series against Cleveland, was 3-for-10 from the field. ... The Pistons are 3-3 on the road in the playoffs. ... Hamilton, Detroit’s leading scorer in the playoffs, had just three points in the first half and finished with 15. ... New England Patriots coach Bill Belichick was at the game, sitting near the Pistons bench. He received a rousing ovation and a chant of “Bel-i-chick!” every time he was shown on the scoreboard. ... Detroit, which set an NBA record with just three turnovers in its series-clinching win last week against Orlando, had three in the first quarter and seven in the third.