LeBron James said the Brooklyn Nets' Joe Johnson "torched" him for a game-high 34 points.

In the end, however, James and the Miami Heat extinguished the flickering flame that represented the Nets' season.

Backed by a 12-0 run in the final minutes, the Heat advanced to the Eastern Conference finals with a 96-94 victory over the Nets on Wednesday night at AmericanAirlines Arena.

The Heat, who beat the Nets in five games, now await the winner of the other Eastern Conference semifinal between the Indiana Pacers and the Washington Wizards. The Pacers lead the best-of-seven series 3-2.

As for Johnson, the Brooklyn shooting guard who made 15 of 23 shots, including three of six 3-pointers, Heat coach Erik Spoelstra tried to encourage James.

"Joe Johnson was a handful," Spoelstra said. "We kept telling (James), 'Stay with it.'

"(Johnson) was making tough shots over the top. We didn't want to send another defender because of their 3-point shooting. (James) made a couple of big-time stops at the end by not panicking or overreacting."

After a 20-foot jumper by Johnson, the Nets led 91-83 with 4:49 left in the game.

That is when the Heat made their charge. James, the superstar forward who led the Heat with 29 points, made a 3-pointer. Guard Dwyane Wade, who had 28 points, added a 10-foot jumper.

Johnson then finally missed. He was off target on two jumpers in a row, and James hit two free throws to bring the Heat within 91-90 with 1:12 left.

The Heat took the lead on a 3-pointer with 32 seconds left by guard Ray Allen, who took a feed from point guard Mario Chalmers.

"I was going up for the shot," Chalmers said. "But when I caught it, I knew (the Nets) had to make a decision between me and (Allen). They closed out on me, and I was able to find Ray.

"That's a great option when you know you have the all-time greatest 3-point shooter to your left."

Nets guard Shaun Livingston then missed a shot in the lane, and Heat forward Chris Bosh grabbed the rebound with 22 seconds left.

"There were some fouls out there," Livingston said of his bank shot that rimmed out, "but I'm not going to cry over spilled milk."

After two free throws by Allen, Johnson cut Miami's lead to 95-94 with a 3-pointer.

James followed by making one of two free throws to put Miami up 96-94 with 9.5 seconds left.

The Nets lost possession with five seconds left when James slapped the ball out of the hands of Brooklyn forward Paul Pierce. However, the call was overturned, giving the Nets a final chance.

Johnson took a pass and dribbled toward the foul line, but James and Allen stole the ball to preserve Miami's win.

"I was in a crowd," Johnson said of the defense, "but it shouldn't have even come down to that. We didn't execute down the stretch offensively or defensively."

With the win, the Heat improved to 9-0 in the "Big Three" era of James, Wade and Bosh in home games in which they had the opportunity to close out a playoff series.

In addition to Johnson's contributions, the Nets got 19 points from Pierce and 17 from point guard Deron Williams.

Johnson had 12 points in the third quarter as the Nets outscored Miami 26-24 and padded the seven-point lead they held at halftime. The Nets went into the fourth ahead 75-66.

There were 13 lead changes in the first half, but the Nets were up 49-42 at the break.

Cold-shooting Miami shot 34.1 percent from the field in the first half, including one of 16 on 3-point attempts.