The Heat did not have it all their own way, though, and had to rally from an 11-point second-half deficit to defeat the Bulls 94-91 to clinch the semi-final series 4-1.
Carlos Boozer contributed 26 points and 14 rebounds but it was not enough for the Bulls, who had taken a 1-0 lead in the best-of-seven series but were dogged by injuries.
"It's a shame," Heat coach Erik Spoelstra said on the Bulls
"I think everybody wanted to see both teams healthy. You survive and move on ... We all know they've gone through a great deal of adversity. Everybody wanted to see both teams compete."
Trailing by 11, the Heat went on a 10-2 run late in the third quarter and the beginning of the fourth. It got them back into the game before the strong finish.
"It is sort of the story of the season," Bulls coach Tom Thibodeau said.
"Obviously, we're disappointed in losing the series, but I was never disappointed in the team. I thought our team fought hard all year long."
The Memphis Grizzlies also secured a 4-1 series win on Wednesday night, toppling the Oklahoma City Thunder 88-84 to reach the Western Conference finals for the first time in franchise history.
Zach Randolph had 28 points and 14 rebounds for the Grizzlies.
Kevin Durant poured in 21 points for the Thunder, but missed a 15-foot jumper which would have tied it in the final seconds and the West's top seeds crashed out.