Use Invalidations to clear the cache, you can put the path to the files you want to clear, or simply use wild cards to clear everything.
This can also be done using the API! http://docs.aws.amazon.com/cloudfront/latest/APIReference/API_CreateInvalidation.html
The AWS PHP SDK now has the methods but if you want to use something lighter check out this library: http://www.subchild.com/2010/09/17/amazon-cloudfront-php-invalidator/
user3305600's solution doesn't work as setting it to zero is the equivalent of Using the Origin Cache Headers.
~ Answered on 2014-12-02 03:22:20