The Heat had lost all four meetings with the Nets during the regular season, but the two-time defending NBA champions have been dominant in the play-offs, improving to 5-0 after whitewashing Charlotte in the opening round.
LeBron James led the way with 22 points, Ray Allen scored 19 off the bench and Miami outsourced Brooklyn 61-43 in the second half to run away with the win.
"(The Heat) has been waiting on us," said Nets veteran Kevin Garnett.
"They have been resting. They have been hearing that we beat them this and all that. We need to be better, and we will be."
Nets forwards Paul Pierce (eight points) and Garnett (zero points, four rebounds) were non-factors in the renewal of their fierce playoff rivalry with James.
While members of the Boston Celtics, Pierce and Garnett faced off against James in four different play-off series with each side winning twice.
"I told (Pierce before the game) that it feels right," James said, of facing his rival once again. "I've been in nine postseasons, and I've played him in five. He's one of the best guys that I love competing against."
Brooklyn struggled to keep James and his team mates out of the paint where the Heat scored 52 points.
The Nets trailed just 55-52 early in the third quarter before Miami exploded for a 15-2 run and never looked back.
Chris Bosh finished with 15 points and 12 rebounds for the Heat while Dwayne Waded added 14 points.
Joe Johnson and Deron Williams scored 17 apiece to lead the Nets.
Game Two of the best-of-seven series is on Thursday, again in Miami.
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The San Antonio Spurs continued their return to top form with a 116-92 rout of the Portland Trail Blazers on Tuesday in Game One of their Western Conference semi-final.
Tony Parker blazed the trail with 33 points and nine assists to give San Antonio the 1-0 lead in the best-of-seven series.
It was the second consecutive blowout win for the number one seed Spurs, who blasted Dallas by 23 points on Sunday in the deciding seventh game of their surprisingly tough first-round series.
Parker set the tone against Portland with his aggressive play, insisting he was not motivated by his premier point guard matchup against young Blazer Damian Lillard who had 17 points.
"Lillard is a top guard in the NBA. I just try to be (San Antonio coach Gregg Popovich's) favorite point guard," Parker told reporters.
"I'm always going to try to do my job and be aggressive."
The Trail Blazers entered the night riding high, having eliminated Houston 4-2 in their opening matchup to reach the second round for the first time in 14 years.
But the home Spurs pounded Portland in the first half to take a 65-39 lead into the halftime and the Blazers could not recover.
LaMarcus Aldridge sustained his great play during the post-season with 32 points and 14 rebounds, but it was far from enough for the Blazers.
"Most of our guys haven't been (this far into the playoffs) so this lets us know how it's going to be," Aldridge said. "It's a learning process, the intensity that championship teams play with."
San Antonio reserve Marco Belinelli had 19 points and Tim Duncan added 12 and 11 rebounds in a complete team effort.
Game Two is on Thursday in San Antonio.
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