The Heat actually have on of the higher rated interior defenses in the league. There was a nice article I read a few months back detailing the stats, I'll see if I can find it. The jist of it was that though they lacked a true dominant center, they had great length at every position and play some of the best weakside defense out there.
The Bulls just aren't that good of an offensive team, their games all playoffs long have demonstrated that fact. Getting hot from 3 point range isn't something you should count on. Interesting debate during the game between Miller and Kerr about Kyle Korver, he was getting burned badly on defense and Miller thought he should be pulled (I agree). Kerr thought Korver had to be out there to stretch the defense and provide some offense for the Bulls.
Pretty much all the 50/50 calls went the Bulls' way, that usually happens at home with the crowd feeding the refs. If this same game was in Miami it would have swung heavily in the Heat's favor with those calls.
I felt the Heat would split the first two games on the way to winning in 6. Spo made the right adjustments and now it is on Tibs to respond for game 3. His reluctance to pull Korver in those final 5 minutes as the Heat exploited him nearly every trip down the court was sad to watch. He has the X's and O's down defensively, but he still ignores the offense and seems to have a poor grasp of momentum. He works his guys hard, and their record this year is a testament to that fact. However, I think he has worked them too hard (Scott Skiles, Avery Johnson type) so that they don't have another gear to hit when times get tough. For as hard as he pushed them all season to secure homecourt, they just lost it tonight.
Finally, if Boozer keeps struggling to put up a double double or even a single double, the Bulls have no chance.