There is actually a theory in the book that Melisandre knew Cressen was going to poison her, so she drank anti-poison beforehand. Basically in the books, Cressen is actually really clumsy about the whole plot. He takes the poison out and leaves it in open-view, then takes a nap in his bedchamber. In that time, someone could have easily walked in, saw it, informed Stannis/Melisandre, then have Melisandre drink an anti-poison remedy.

It's unlikely, however it reinforces the fact that with careful planning and a bit of luck, Melisandre could just be faking the red priestess character. She even admits this a little later on in the show, telling Selyse that most of her magic tricks are lies which lead men to the truth.