Not an idiom, but a single word could be...
- something advantageous or valuable that is received or obtained as a benefit beyond what is due or expected. (Dictionary.com)
To cite an example, I'm reminded of a line of Charlie's from 2½ Men:
"Alan, he was happy to see his friends. Being away from you is just gravy." (=unintended benefit)
If the benefit is financial, you could also use...
an amount of money that somebody/something wins or receives unexpectedly (ODO)
EDIT: Like @Tim said, this can also be used metaphorically to refer to gains other than financial, but it doesn't quite convey the 'unintended' part.
If you're looking for an idiom, rather than a single word, consider:
pennies from heaven, a stroke of luck
But, again, these don't quite cover the 'unintended result of your own action'.