MIAMI (AP) — Dwyane Wade made what seemed like the perfect play. Rajon Rondo came up with something better.

Rondo scored 25 points, including a buzzer-beating layup after catching Paul Pierce’s lob at the end of regulation, then delivered the biggest shot of overtime as the Boston Celtics got a wild 112-106 overtime win over the Miami Heat on Wednesday night.

Wade’s steal and dunk with 0.6 seconds left gave Miami a two-point lead, part of his season-high 44-point effort. But Rondo spun clear to catch Pierce’s perfect pass and laid it off the glass to tie the game, then sealed the outcome by knocking down a short floater with 34.3 seconds left in the extra session.

“To just keep believing, what a great win for us,” Celtics coach Doc Rivers said.

And from the other end of the arena, the Heat offered the exact opposite view.

“It really gets no tougher than this one,” Wade said.

Ray Allen scored 22 points and Kendrick Perkins added 20 points and 10 rebounds for Boston, which trailed by 11 midway through the fourth quarter. Pierce scored 17 and Rasheed Wallace added 16 for Boston, which was outscored 26-4 in points off turnovers and lost the offensive rebounding battle 17-5.

“We found a way,” Rivers said. “A lot of guys did a lot of little things for us.”

Udonis Haslem scored 19 off the bench for Miami, and Jermaine O’Neal added 14 for the Heat.

“Bottom line is, we had our chances,” Haslem said.

There was no way overtime would live up to the end of regulation.

Miami missed 15 of 16 shots in the final minutes, which is how the 11-point Heat lead with 7½ minutes left became a four-point deficit with 53.1 seconds remaining in regulation. Allen’s 3-pointer gave Boston an 99-95 lead, and the Heat looked to be out of chances.

Then Wade did what he does best – pull off something spectacular.

His two free throws with 5.5 seconds left in regulation tied the game. On the ensuing inbounds pass, he stripped Allen at midcourt, driving in for a two-handed dunk with 0.6 seconds left to give Miami a 101-99 lead.

Rondo answered, saving the Celtics.

“That play could happen to anyone,” said Mario Chalmers, who was guarding Rondo.

Maybe, maybe not. With 0.6 ticks left, the pass, the catch and shot all had to be perfect – and Pierce and Rondo made it look easy.

“We’ve been working on that play for a long time, actually since last year,” Rondo said. “As soon as Wade stole the ball, I knew exactly that was the play we were going to run.”

The shifts were seismic in the second half, Miami looking like it was in total control after a 28-9 run put the Heat up 89-78 with 7½ minutes remaining, then wasting it as Boston answered with a 21-6 burst of its own, capped by Allen’s 3-pointer late in regulation.

Almost forgotten in the frantic finish was a play with 1:35 left that gave Boston a huge break.

Quentin Richardson got tangled up with Pierce and called for a foul, then argued so vehemently that he was hit with a technical. Allen made the ensuing free throw, a point that the Heat certainly would have loved to have back at the end of regulation.

Richardson wouldn’t talk about the call.

“They scored with 0.6 seconds. That’s tough to swallow,” Richardson said.

Pierce returned after missing five games with a right knee infection, and Rondo played after sitting one game with a sore left hamstring. Kevin Garnett (sore right knee) remained sidelined for the third straight game; he shot 11 of 12 in the teams’ only other meeting this season – a 92-85 Boston win on Nov. 29.

“The sum of our parts is what makes us great,” Allen said. “When somebody goes down, somebody else has to step up and other guys have and will in the future. Anytime you lose a guy, you miss them and feel the weight of it.”

Wade had 25 points in the half, and the Heat needed every one. Even with Wade’s scoring blitz, the Celtics still led 57-54 at the break.

The Celtics’ lead was eight midway through the third, before the Heat put together their best stretch of the game to end the period. Haslem and Wade combined for 10 points in a 17-6 Heat run, and Miami took a 78-75 edge into the fourth.

And when Wade came back in with 7:54 left, the second unit had done its job for Miami, stretching the edge to 87-78. Of course, then the Celtics were just getting started, and Miami eventually left for a six-game Western Conference road trip off perhaps its most draining loss of the season.

“Not going to sleep tonight, I’m sure,” Wade said.

NOTES: Miami kept the ball for 1 minute, 12 seconds during one fourth-quarter possession, missing five shots on the trip. … Heat G Carlos Arroyo’s contract became guaranteed for the remainder of the season, since Miami did not waive him by a 6 p.m. Wednesday deadline.