Luke 4:33-35 (NKJV)
Now in the synagogue there was a man who had a spirit of an unclean demon. And he cried out with a loud voice, saying, "Let us alone! What have we to do with You, Jesus of Nazareth? Did You come to destroy us? I know who You are--the Holy One of God!"
But Jesus rebuked him, saying, "Be quiet, and come out of him!" And when the demon had thrown him in their midst, it came out of him and did not hurt him.
I find it interesting that the demon spirits are not deceived. They know who Jesus is and they are subject to Him obeying instantly when Jesus commands them. I wish many people I know were as knowledgeable of truth and as subject to authority as the demons are.
Satan has authority over this world which he acquired when Adam gave up the authority God had originally given to him. But God still has authority over all of creation. God, being the righteous sovereign he is, allows Satan to run his course. However, God defeats Satan and defends his holy Name, not by wiping Satan out, but by being both righteous Judge and by taking upon himself the penalty of our sin. This makes it possible for both justice to be satisfied and for us (sinners declared righteous by God's own sacrifice) to live with Him in eternity.
Romans 3:23-26 (NKJV)
For all have sinned and fall short of the glory of God, being justified freely by His grace through the redemption that is in Christ Jesus, whom God set forth as a propitiation by His blood, through faith, to demonstrate His righteousness, because in His forbearance God had passed over the sins that were previously committed, to demonstrate at the present time His righteousness, that He might be just and the justifier of the one who has faith in Jesus.