A chick is giving you a hand job with gobs of vaseline and right when you are about to cum she shoves her mouth around your cock causing vaseline to fill her mouth and push up her lip giving her a vaseline mustache. It may be dirty but it gets the job done.
Can also be used as a nick name.
"That chick from the bar last night is a Dirty Melissa."
I though all she was gonna do was give me a hand job but then she went a bust out the Dirty Melissa it was fucking awesome!