BY TIM REYNOLDS
AP BASKETBALL WRITER
MIAMI (AP) -- Turns out, the Miami Heat can beat the Brooklyn Nets.
And rest hardly led to rust for the two-time defending NBA champions.
LeBron James scored 22 points, Ray Allen added 19 and the Heat stayed perfect in this postseason by beating the Nets 107-86 on Tuesday night in Game 1 of an Eastern Conference semifinal series. It was the first win for Miami in five meetings with Brooklyn this season.
Chris Bosh scored 15 points and grabbed 11 rebounds, Dwyane Wade finished with 14 points and Mario Chalmers had 12 for Miami, which recorded at least one regular-season win against every team except Brooklyn, losing four times by a total of 12 points.
This one was a different story.
Deron Williams and Joe Johnson scored 17 points each for the Nets, who got only eight from Paul Pierce and no points from Kevin Garnett in 16 minutes.
Game 2 of the best-of-seven series is Thursday night.
A 24-9 run in the third quarter blew things open for the Heat, who hadn't played in eight days after sweeping Charlotte in the opening round. James finished 10 for 15 from the field and Allen - who had never faced his former Boston "Big 3" compatriots Pierce and Garnett in the playoffs - was 4 of 7 from 3-point land.
Miami's lead was 55-52 early in the third quarter after a 3-pointer by Williams, and every indication was that the Heat and Nets - who played three one-point games and a double-overtime affair in the regular season - were heading down to the wire again.
The Heat took off on the 24-9 run over a 7-minute span, with Bosh scoring the first seven points of that burst to get Miami going. Allen's 3-pointer pushed the lead to 14, James and Chris Andersen (who left in the fourth with a right knee contusion) added two free throws apiece and just like that Miami's lead was up to 79-61.
For Brooklyn, it was a collapse at an unexpected time. The Nets had the best third-quarter scoring differential in the East after Jan. 1, but were outscored 33-23 in that pivotal quarter in Game 1.
It was a hectic news day long before Heat-Nets, with Oklahoma City's Kevin Durant being announced as the league's MVP, the firing of Golden State coach Mark Jackson and the NBA saying that Los Angeles Clippers president Andy Roeser would be taking an indefinite leave as part of the fallout related to the Donald Sterling scandal.
And pregame lineup moves by both clubs lent more intrigue. Miami brought Shane Battier - who played 2 minutes, total, in the first round against Charlotte - back into the starting five, while Brooklyn reinserted Shaun Livingston into its lineup after using him off the bench late in the Toronto series.
After never leading by more than seven points against Brooklyn in the regular season, the Heat led by 11 after a drive by James with 3:32 left in the first half. But the Nets closed on a 14-6 run, and Williams' first beat-the-clock 3-pointer of the game sent Brooklyn into halftime down 46-43.
Williams did it again in the third, but that one only got Brooklyn within 79-66.
NOTES: The Heat held a pregame moment of silence for Hall of Famer Jack Ramsay, who died last week at the age of 89. ... David Beckham, who will be bringing an MLS team to Miami, sat next to the Heat bench. ... Livingston was on the court to warm up for the second half with about 10 minutes left in the intermission. Small problem: The rack of basketballs wasn't on the court yet. ... The Nets are 1-9 all-time against Miami in playoff games. ... Miami had not won consecutive Game 1s since the 2nd and 3rd rounds of the 2012 playoffs.