He knew the spell, he had the intention and he said the incantation. The wand was just inches from his hand and it worked.
He had quite a strong connection with his wand by this point and they are described as "quasi-sentient." His wand also defends Harry pretty much by itself when Voldemort attacks him with Lucius Malfoy's wand because it recognised the enemy and the need.
Also the spell is quite simple, so I think that helps. Could he have conjured a patronus or transfigured something in that same situation? I think that would be completely different.