Montag's capture was farce performed by the government so they could retain supreme control over all civilians. They considered him an enemy of the state, & treated his chase as such. In order for a government to maintain totalitarianism, the citizens must be united against a common enemy. In this case, Montag. During times of war, it is important for enemies to be captured, as proof of the government's competence, power, and righteousness. This works even in democracies-think of the furor surrounding the capture of Saddam Hussein, & imagine the celebration in the United States at the capture of Osama Bin Laden.
In the book however, the government cannot afford to be wrong. In order to keep the citizens content and unthinking, those in power must be right every time. Thus, they fake Montag's capture, keeping the populace happy and unified. They can say that no enemy ever escapes, and no one will question that fact. Even though Montag is truly free, the power lies with everyone thinking he is gone. The government sees no harm in having him escape, because they feel he can do no damage. Plus, their reputation remains intact.