I always thought since its suppose to burn until the target is gone petty much that he just focused really hard on Karin being gone so they just went out the same with bee.I sincerely doubt that :sasuke: Sharingan ability is simply to counter Amateresu...
It's possible that he used his sharingan's ability to stop it, but we still don't know exactly what that ability is. It could be like Kakashis, and he just sent the flames to another dimension... Or it's possible that Itachi had the ability to put it out all along, and Sasuke just figured out how to do it.
My point is, we're still in the dark about what Sasuke's sharingan ability truly is.