Boston led by as many as 17 in the third quarter, but Hamilton scored 13 points during a 21-8 Detroit run that made it 92-88 with 4:46 left.

Boston led 100-96 before Rodney Stuckey hit a 3-pointer with 1:22 left. But, after a timeout with 6 seconds left on the shot clock, Allen took the inbounds pass and put up a jumper to give Boston a three-point lead.

Billups tried an off-balance layup that missed, but in the fight for the rebound the Celtics tipped it out of bounds. Billups drove again, putting it harmlessly off the front of the rim.

The Celtics ran down the 24-second clock before Garnett was forced to take an off-balance jumper. Rondo fouled Stuckey, who hit both free throws to make it 102-101 with 8.2 seconds left.

Allen matched them, then Rondo again wrapped up Stuckey. But this time the rookie missed the first, giving the Boston Garden crowd a reason to erupt.

Garnett hit a pair of free throws to clinch it.

Special feature Luck of the Irish How the Celtics went from worst to first in one year

The Celtics earned home-court advantage with an NBA-best 66-16 record in the regular season, but the Pistons took it away with a victory in Boston in Game 2. The Celtics swiped it back with a split in Detroit, and now have two chances to clinch — including a potential seventh game at home.

Detroit trailed 23-20 in the final minute of the first quarter before scoring 13 of the next 15 points. The Pistons still led 42-36 with five minutes left in the second when Boston scored 11 in a row, getting back-to-back 3 pointers from Paul Pierce and Allen to take the lead for good.

Garnett added a fallaway 3-point bank shot at the 24-second clock buzzer — just his second 3 pointer of the season — to give Boston a 50-43 lead with 1:23 left in the half. Perkins had two of the first three baskets in the second half to extend the lead to 11 points.

Allen added consecutive 3-pointers midway through the third to turn an eight-point game to a 14-point lead.

Notes: Rasheed Wallace picked up a technical with 5:18 left in the game. It was his sixth of the postseason, and his next earns him a one-game suspension. He criticized the officials afterward in an expletive-filled tirade, saying, “A lot of those foul calls, cats were flopping and falling all over the floor.” ... It was Perkins’ 17th double-double in his career and the third time he has had one in the first half. ... The Garden scoreboard operators have figured out how to fire up the crowd: Show Patriots coach Bill Belichick on the scoreboard. ... Brian Scalabrine was active for the first time in the playoffs because Tony Allen injured his Achilles’ tendon during practice on Tuesday. ... Wallace was 3-for-27 on 3-pointers in his previous eight games. ... Detroit’s Game 4 hero, Antonio McDyess, fouled out with five minutes left and scored just four points.