Pierce scored 23 points while Rondo added 15 points and 15 assists as the Celtics evened the best-of-seven Eastern Conference final at 2-2 with game five on Tuesday at Miami and game six back in Boston on Thursday.
Either the Heat or the Celtics will face the Western Conference champions, the San Antonio Spurs or Oklahoma City Thunder, in the NBA Finals starting on June 12.
After regulation time ended deadlocked at 89-89, stars became spectators as Pierce fouled out, collecting his sixth violation 38 seconds into over-time to foul out for the third time in five playoff games.
“When your leading scorer goes out, you have got to step up and make plays,” Rondo said. “That’s what we did.”
Miami’s LeBron James, who scored a game-high 29 points, fouled out with 1:51 remaining, the first time he had fouled out since leaving the Cleveland Cavaliers and joining the Heat two years ago.
“It was like chess. They took our queen and we took their queen,” Celtics guard Ray Allen said. “All that has to happen is the game has to be won. It doesn’t matter what it looks like.”
Kevin Garnett added 17 points and 14 rebounds for the Celtics while Allen contributed 16 points. Dwyane Wade scored 20 points for Miami while Udonis Haslem had 12 points and 17 rebounds for the Heat.
Haslem’s slam dunk gave Miami a 91-89 lead early into over-time.
But Boston’s Marquis Daniels hit 1-of-2 free throws and Rondo sank a jumper to put the Celtics on top 92-91.
Rondo also made 1-of-2 from the free throw line with 21.4 seconds to play to give Boston a 93-91 edge with Miami taking the ball.
Wade elected to try a 3-point shot for the victory and evaded Daniels to create an open opportunity beyond the arc.
“I thought it was going in when it left his hand,” Celtics coach Doc Rivers said.
But Wade’s shot clanked off the rim and the final buzzer sounded.
“We knew they were going to Wade,” Rondo said. “We played good defense on him and got the stop. We executed offensively, came up with some lucky plays and got some stops at the end.”
James, the NBA Most Valuable Player still searching for his first NBA title, was fuming in the locker room about the foul calls that forced him to the bench with the outcome still undecided.
“I don’t foul out,” James said. “That sixth foul, I wish I had earned it. It would have been a foul (by) me. I know how to play basketball. I don’t need the advantage of pushing somebody down or holding somebody, but whatever.
“We have to build off our mistakes, off good and bad things from the last two games. We’ve just got to come out with a sense of urgency. The last two games they have hit us hard. The post-season is all about adversity.”
The Celtics led by as many as 18 points in the first half and 16 in the third quarter.
“They hit a lot of shots in the first half,” the Heat’s Mario Chalmers said. “Our defense wasn’t as crisp as it normally is. In the second half we turned it up. We just kept trying to push the ball, get back into our game.”
The Heat took a 76-74 lead early in the fourth quarter with a 15-1 run that was capped by a layup from rookie Norris Cole.
“We came out in the second half and tried to throw knockout punches,” Rivers said. “Our execution in the first half was flawless, as well as we’ve ever had. In the second half, we got away from that and Miami took us out of our air space.”
Garnett sank an inside shot for an 89-86 Boston lead but James answered with a 3-pointer 15 seconds later to pull Miami level again. The Heat had the final shot of regulation time but Haslem missed a jump shot at the buzzer.
“No one said this was going to be easy,” Heat coach Erik Spoelstra said. “In the second half we got into the grind and into the fight,” he added.
“It was a heck of a half but it wasn’t a heck of a game.”