Look, the Heat probably win this game going away, because the Bulls don't seem to have nearly enough offense to hang with Miami. That said, if they rally and win the game it likely comes down to the defense and rebounding of Joakim Noah and Taj Gibson combined with some hot shooting from the perimeter.
The Heat will almost certainly shoot a higher percentage than the Bulls. Like Chicago, they have athletic defenders they can put on the floor to clamp down on defense, however, they have far better offensive players to overcome the opposing defense played on them. Nothing new there, this is fairly straight forward.
However, while Miami will almost certain shoot a higher percentage than Chicago, what Chicago can do is outrebound the hell out of them. If Chicago can have one of its elite rebounding nights where they are able to throw up 10-12 more shots (adjusting for free throws) then they no longer need score as efficiently as Miami. They can make up for a lack of efficiency by volume of attempts.
The other easy way to make up for a lack of efficiency is to get hot from beyond the arc. The Bulls aren't loaded with great shooters, but if they're able to get offensive boards then frequently that results in a defensive breakdown immediately following the rebound. This allows for put backs, or when the put back is well defended the kick out to an open shooter as the opposing defense scrambles.
This was actually Kyle Korver's most effective way of getting three point shots off for Chicago when he was here, and the Bulls need Belinelli, Robinson, and Deng to look for that open three when Taj or Noah corral an offensive board. The Bulls aren't going to miraculously start knocking down heavily contested threes off the dribble (well maybe Nate on a good day) but they can hit a high percentage if they're able to generate quality looks.
The key to defending the Heat is a quality offense. Miami brings one of the most dangerous transition games in the history of the NBA to the table. LeBron James can't be stopped, slowed, or bothered in the open court. It takes a full five guys clogging up the court to have a hope of him not dunking on you. When Miami generates turnovers or transition looks off of long rebounds, their offense becomes very difficult to defend.
When Miami is forced into the half court, they certainly don't become stagnant or mediocre, but they do go from unstoppable to very good, and the Bulls defense, at its peak, can slow down "very good".
Will Chicago put together the perfect game to dethrone Miami? I'm not holding my breath, but Chicago's effectively beaten the Heat three times without Rose already, so it can be done.