Rondo will have surgery for a torn anterior cruciate ligament in his right knee. He was hurt late in Boston's 123-112 loss, also in two overtimes, to the Atlanta Hawks on Friday night.
The postgame mood in the locker room "was good" before he told his players the extent of the injury, coach Doc Rivers said, "and then it went down."
This game was the first in Boston for Ray Allen since he left the Celtics after five seasons and signed as a free agent with Miami. He scored 21 points.
Kevin Garnett had 24 points and 11 rebounds, and Pierce added 17 points, 13 rebounds and 10 assists for the Celtics, who ended a six-game losing streak, their longest in six seasons. LeBron James had 34 points for the Heat, whose winning streak stopped at four.
"As much as I've been a rival with Boston over the years, I never want to see anyone go down," James said. "It's terrible, not only for their team but for the league."
Pierce's basket gave the Celtics a 99-98 lead. James had a chance to put the Heat ahead but missed a 12-foot jumper with 6.8 seconds to go from the left with defender Jeff Green jumping out at him. Pierce got the rebound and was fouled.
He sank the first shot. Then, as a fan shouted, "This one's for Rondo," he missed the second.
Miami had one last chance, but Shane Battier missed a long jumper at the buzzer.
The Heat also could have won in the first overtime, but Dwyane Wade, who had 17 points, missed a long jumper as the buzzer sounded. They had led 93-89 after consecutive baskets by James, but Garnett hit a layup with 1:45 remaining and a shot from the right baseline with 1:14 to go.
Boston could have avoided the first overtime when Pierce inbounded from behind his backboard with two seconds left to Jason Terry. But Terry's shot from the top of the key was short. The Heat had tied it on a 3-pointer by James with seven seconds remaining in regulation after Allen missed a 3-pointer from the left corner with 15 seconds to go.
Rondo arrived at TD Garden on Sunday for a pregame shootaround but was taken to a hospital after complaining of knee pain. Courtney Lee started in Rondo's place.
The initial report was a hyperextended knee, but the team announced during the game that tests showed the ACL tear. His teammates didn't find out until after the final buzzer.
Allen was part of the Big Three with Pierce and Garnett starting in 2007-08. In their first season together, Boston won its 17th NBA championship. He played against the Celtics once before this season, a 120-107 Heat win in Miami in the opener.
The crowd gave Allen a standing ovation when highlights of his career with the Celtics were shown on the video board above center court during a timeout with 5:33 left in the first quarter. At the Miami bench, he raised his left hand in recognition.
Allen entered the game about a minute later and was booed when he touched the ball. The boos came down again when he took two free throws -- missing the first, making the second -- three minutes into the second quarter.
Allen went back into the game with 30 seconds left in the first half with the score tied at 43 and made a layup with 16 seconds to go. But Pierce sank a driving layup with 4.3 seconds remaining to tie it 45-45 at halftime.
It was Miami's first game in Boston since it won Game 6 of the Eastern Conference finals behind James' 45 points.