Rey clearly already knew how to fight. We saw her beat up those guys with her staff on Jakku. Why would fighting with a lightsaber be that different? If anything, it would be easier: surely a lightsaber is super-light, what with the hilt being the only physical element of the whole shebang.

That combined with Kylo's heavily injured condition, the fact that he wasn't trying to seriously hurt her but rather turn her to the dark side and her digging into the force made it seem completely believable that she would beat him.