After describing the Christian's spiritual armor Paul then emphasizes the importance of prayer. It is instructive to examine the nature of that prayer. Victory over a demonic hierarchy involves persistence in talking to God. By praying for one another, Christians battle demons. In the next two verses, Paul requests prayer twice for himself as a missionary.
Prayer empowers the preaching of the gospel.
Maybe this is what happened in Northampton, Massachusetts where a monument states that there Jonathan Edwards encountered the Devil and defeated him. In Ireland, Patrick encountered the druid witches, and the Celts recognized God's power as superior. History notes that following both events, multitudes turned to Jesus Christ. These men spent considerable time with God, but I've never seen any record of their talking to the Devil. Biblically and historically, then, spiritual battles are won by living for God and talking to Him in earnest intercession rather than by talking to Satan.