Reserve guard Ray Allen hit a 3-pointer with 32 seconds left to give Miami its first lead of the fourth quarter at 92-91. Nets guard Shaun Livingston then missed a shot in the lane and Heat forward Chris Bosh grabbed the rebound with 22 seconds left.
Nets guard Joe Johnson, who had a game-high 34 points, cut Miami's lead to 95-94 with a 3-pointer. Heat forward LeBron James followed by making one of two free throws to put Miami up 96-94 with 9.5 seconds left.
The Heat, which beat the Nets in five games, now await the winner of the Eastern Conference semifinals between the Indiana Pacers and the Washington Wizards. The Pacers lead the best-of-seven series 3-2.
There were six lead changes in the first quarter, and the Heat ended up on top, 23-22. However, it was an atypical Heat quarter -- the NBA's top-shooting team made just 35 percent of its shots from the field despite 12 points from Wade.
Brooklyn, with nine points from Pierce, shot 50 percent from the floor.
NOTES: It is possible that this postseason marks the end of the 19-year NBA career of Nets C Kevin Garnett, who turns 38 on Monday. Garnett averaged a career-low 6.5 points in the regular season. In the opener of the Heat series, he was held scoreless in a playoff game for the first time in his career. ... The future of Nets F Paul Pierce, 36, also is uncertain. He will become an unrestricted free agent on July 1. ... In a statistical oddity, reserve G Ray Allen led Miami in rebounding twice in the first four games of this series. ... Heat G Dwyane Wade, who was rested repeatedly in the regular season, is healthy now. He has yet to miss a postseason game and is averaging 34 minutes.