I had a couple of similar kills with bows (mostly northern bow). The one I consider the luckiest, was one-shot kill of the large stag, who was exactly at the border of visible screen, with maximum zoomout - i.e. the longest distance of shooting. My guy was quite a crappy shooter then, so I was surprised when he instakilled the stag with single try. In this case it was thorax, not eye shot, with a broadhead arrow.
I also had some intakills with humans, and other deer.
Quite often I have instakill of birds with thrown spear, but this is easier to do, since the distance is smaller than with bow.
I also had something which can be considered luckiest in another sense, when I wasn't targeting the subsequent kill. I shot at the stag, and missed, the arrow flew past the screen border. When I went there looking for it, I found it quite further, together with a badly damaged corpse of a goshawk (it was a broadhead, so nothing strange there). This way I learned that the ballistic curve and collision detection is calculated even for off-screen objects. Since then I was using this technique to shoot these nasty robbers from afar.