I heard a sermon once that pointed out that Shadrach, Meshach, and Abed-nego went into the fire bound and came out loosed. The message was that it's in the very trials the Lord brings us through that we are set free, and I know there's truth to that. However, there's another way to look at it.
"But these three men, Shadrach, Meshach and Abed-nego, fell into the midst of the furnace of blazing fire still tied up" (v. 23). The furnace they were thrown into was seven times hotter than usual, so hot that the people who carried them up to the furnace died. Why did the heat also not kill them on their way into the flames?
It seems likely to me that the Lord was already waiting for them in the flames when they were thrown in. I suspect it was His presence, not simply His intervention, that made the difference. I also believe, and from things I have seen recently I am convinced of this, that it was Lord Himself who untied them, by His own hand. They weren't so much set free in and through the fire as they were set free by the God who allowed the fire and met them in it.