There is no blow by blow report of the 'fight' between Dorn and Curze. We do know that Curze confided in his old teacher Fulgrim, when Fulgrim found him fitting, of the visions that had plagued him and how the Imperium was doomed.
Fulgrim in turn told Dorn, who had already had strong words with Curze previously about his actions upon the Cherott (sp?) system. Dorn took offence to this slight on the Imperium and in turn the Emperor, and went to confront Curze once again.
During the confrontation, Curze was wracked by his painful visions/seizures, and when he regained his senses, he was stood over the body of Dorn, having ripped chunks out of him with his bear hands and teeth, almost killing him. Sigismund, who later go on to be the first Emperor's champion and found the Black Templars, was the first to arrive at the scene, but no one other than Dorn really knew what happened.
We do know the attack did have a lasting psychological effect on Dorn, as such an act of unexpected violence would, but it is never said to the best of my knowledge what actually took place, whether Dorn had a chance to defend himself or not, or if Curze just leapt on him and bloodied him before Dorn even knew what was happening.