Skyrim Dragons Running When Hurt

I would say as Konerak said, get yourself a companion. I got one not that far in the game for free for becoming a thane of something something. And after that me and her killed a lot of dragons together. For some strange reason the dragons always focus more on companions then you. So mostly I stay next to it or behind it and fire arrows at it, while my companion tanks the damage. Doing some of the dark brotherhood quests you get a spell to summon an old ghostly assassin, that might help aswell.

But to do it just you vs a dragon I would say shout a lot and remember the 5 D's : Dodge, Duck, Dip, Dive and Dodge!

I did some looking and there appear to be a good variety of glitches in which dragons can die. Some of them might fit your scenario:

1. Dragon flies (glitches) into ground and dies. Thunder sound, death throes animation, dead. No soul absorbed but this guy was pretty far away and never engaged the dragon:

2. There are a few recorded accounts of dragons dying when they land. This one shows a dragon that was at full HP who lands, dies, and the soul is still absorbed:

3. Same case as before, but the dragon was damaged:

There are plenty of other videos in which dragons die as the result of glitches, but I think that these three best match your scenario out of all of them. Let me know if this helps!

Here is an example of a dragon simply spawning dead in front of a player; the "dead dragon glitch" you mentioned earlier. This one doesn't match your scenario too well, but appears to be fairly common:

For the sake of showing that it appears to be possible, here's a video showing two dragons going at it (uhh... fighting):