Just to paint the whole picture let's go back to the very beginning. The thing about God's sovereign will is that He generally chooses not to enforce it. God created creation, and He was in charge of it. God created man, and yielded His sovereignty to put man in charge of it. His deal with Adam was, I'll walk with you, talk with you, lend you an ear and give you advice, but what you say Adam, that’s what goes. You, Adam, are the authority. So Adam then gives that away to satan. God could have in His sovereign power taken it all back, but then that would put Him back in charge, and that was never His intent, His will. His intent/will was for man to have authority. So to restore what He intended/willed meant a man had to take authority back from satan. But who among us could do such a thing? Well, only God, coming to us as a man. So the Messiah comes and indeed takes back authority. But, He has yet to return to this world to enforce it. That's where our partnership comes in. It is our charge that we participate with Him in the enforcement of His authority over the yet-to-be restored creation. And we do that thru prayer and partnering in the gifts and manifestations of the Holy Spirit.
Maybe a simpler way to look at it is to compare it to a Sheriff and his deputies. The Sheriff is the one who holds authority, but he doesn't actually go out and patrol the streets. His deputies are the ones who go out and enforce the Sheriff's authority. Christ is the Sheriff, it's His authority. But until He returns to lay claim to the land, we are to be His deputies enforcing His will in a land run by criminals.
So while satan in general rules this world, we have Christ's authority to supersede that in the places and things we come in contact with. Because, like Roger said, greater is He that is within us than he that is running the world.