From The Associated Press Stylebook and Briefing on Media Law:
convince, persuade. You may be convinced that something or of something. You must be persuaded to do something.
Right: The robbers persuaded him to open the vault.
Wrong: The robbers convinced him to open the vault.
Right: The robbers convinced him that it was the right thing to do.
Wrong: The robbers persuaded him that it was the right thing to do.
