No, prayer doesn't change things.
The only thing prayer changes is the pray-er's perception of the outcome of what he is praying about. It makes the person who prays believe that everything is now out of his hands, and that he is being watched over. All it does really does is comfort (and blind) a person in need.
Example: A man prays in earnest for the deadly illness befalling his wife to go away. The wife dies, despite his prayers. "Don't worry, my Son. It's all in God's plan." The prayer takes no heat from its failure.
A man prays in earnest for the deadly illness befalling his wife to go away. It does, even though the prayer did nothing for the illness. "God is watching over his children, my son. Prayer changes things." The prayer is seen as a great and powerful tool for the believer.
Dogma.