Miracle. NFL record-setting. Blah blah blah.
It's simple: The Bears' offense was so bad that the only way to win the game was to keep the ball out of their hands.
At the end of the third quarter, with the Bears trailing 3-23, rookie defensive end Mark Anderson forces a Matt Leinart fumble. But the Bears' defense, cognizant of how terrible and turnover-prone their offense had suddenly become, knew that it had to prevent their own offense from touching the ball at all costs. So Mike Brown took it upon himself to grab the loose ball and run it in for the TD. Sure, scoring a TD whenever you can is what all football players try to do. But that wasn't what was motivating Brown at that moment. He knew that scoring the TD himself was the only way to prevent the Bears' offense from giving the ball back to Arizona. He was left with only one choice.
Then in the fourth quarter Brian Urlacher arrives late to a stuffed Edgerrin James run up the middle and strips the ball. Amidst the pile of bodies Charles Tillman sees the loose ball and thinks, "holy crap, if we recover this fumble, our offense will turn it over back to Arizona!" He makes a split second decision: let Arizona recover it (thereby preventing the Bears' offense from giving it back to them anyway and saving precious time on the clock) -or- recover the fumble but be sure to return it for a TD. Falling on the ball and recovering it for the offense was not an option. So, like Brown before him, he took a risk and recovered the ball and sprinted for the end zone.
Whew! If he had been tackled, the Bears' offense would have gotten the ball back. And no one wanted that to happen.
On the ensuing possesion the Bears force Arizona to punt yet again. That's good; Arizona can't score if they don't have the ball. But here's the bad: the Bears' offense will touch the ball and probably turn it over. So the Bears' special teams unit had only one choice: return the punt for a TD and prevent the offense from having a chance to screw up again.
Thankfully Devin Hester was well aware of this. As he began darting up the middle and watching his blocks form he thought, "oh man I better juke that punter, otherwise the offense is going to have a chance to turn the ball over again." Thanks to many great blocks--a pair of which came from Brendan Ayanbadejo--Hester successfully kept the ball out of the offense's hands.
And thus the Bears won.
Not a miracle at all. Simply a matter of the Bears' D and special teams knowing that--no matter what the cost--they could not allow their offense to touch the ball again.