This is a rare occurrence, but can happen. If a vendor seriously needs cash or there's an error regarding the invoice due date, then it will result in an awkward phone call. The important thing to remember is to always check your files. They should have due dates and agreed-upon amounts.
The correct way to handle this is to take the message, go to your manager to discuss the situation, and then follow whatever your manager says. If they're unavailable, go to your files and let them know the due dates you've recorded and the amount due. Don't authorize payment without permission from a manager.