There seems to be a lot of consensus that Korbelus is a really good (high tier) unit to pick in Dota 2, but what makes her so good? All I know is she's rather tanky for an int hero, but other than that her skills seems to be so so, if she doesn't have her ult she can't solo any hero (and her only other contribution to a team fight at that point is a silence with a so-so radius), and if she does have her ult all they have to do is run away for a while.
Death Prophet is a very strong midgame carry with great pushing, which fits her nicely into the current metagame. Her ultimate does absurd amounts of damage, the problem is that she's naturally a rather squishy hero and thus can't effectively stay alive long enough for it to deal damage. She's also rather level dependent and has no escape mechanism, making her in a solo mid role extremely vulnerable to ganks, especially in high tier play. I almost exclusively take her solo mid despite this, however, as she needs the levels and gains a lot of effectiveness from rune control. She's also not great in 1v2 lanes, even the safe lane.
Starting items: 3 branches, +3 INT, +2 all, and Tangos. Rush yourself a bottle and then Arcane Boots as soon as possible, finishing the Talisman and Magic Wand when available. An alternative start is 3 iron branches, 2x +3 STR, and Tangos, which will let you get a quick Urn. Usually there's a better wielder on your team as she's not a great ganker, but this item is stupidly powerful and every team should have one, so pick one up if you don't expect anyone else to.
Use your Wave at x:50 or so to push the lane and control runes- this makes your opponent have to choose between experience from your now advancing creep wave or contesting the rune. If it's invisibility or haste consider ganking; if it's regeneration or illusion use it to gain an advantage in your lane, and if it's DD you can do either. In lane, try to use her Wave to pick up multiple last hits and harass at the same time- the range is enormous but it must be cast carefully. Be very wary of missing opponents and ask for wards if you don't have them, her early game needs to be strong or you'll have a weak midgame.
From there you'll be working towards a Bloodstone, typically picking up the Point Booster and Vitality Booster first and disassembling your Arcane Boots to complete the Soul Booster, which gives great regeneration in and of itself. (I just learned this last trick recently so you won't see it in the replays below.) If you're farming extremely well and don't feel that you need the extra HP, you can pick up the Perseverance pieces first to improve your farming even more. Turn your now plain boots into Phase Boots at some point during this time, or if your team really needs it get another set of Arcane Boots.
When you've finished Bloodstone, you want other stuff that's going to keep you alive. Against heavy physical damage opponents go Blademail, Shivas, or Assault Curiass. Against a singular hard carry go Sheepstick, Cyclone, or Ghost Scepter. Against heavy magic damage opposition go Hood, Pipe, or Heart. Extremely rarely you can consider a BKB, but since her ultimate isn't too affected by disables unless it remains uncast you usually shouldn't worry about it.
Typical skillbuild: QEQWQRQEEERWWW+R ... this rarely changes, the only possible difference might be swapping Silence and E at level 2/4.
In teamfights, her ultimate needs to be used aggressively, because as you pointed out, they can just run away from it. If they chose to run away, you should be getting a free tower, so only ultimate when you need to- if the threat of your ultimate is making the team wary of defending the tower, take the tower for free and keep going. You should be coordinating with your team during midgame to push as soon as possible, usually taking all Tier 1 towers before 15 minutes. The range on her ultimate is huge, you need to be focusing your spirits to deal damage to buildings from afar. If they want to initiate on you, they should have to go through your team to do it. Choose a key target and right click them: your spirits will attack whatever you do. Don't undervalue her silence, at 6 seconds and with an extremely large AoE she's formidable as hell in teamfights. The later the game goes, however, the weaker she becomes. Like most midgame carries, her effectiveness compared to other heroes peaks at level 16, and so if the game lasts more than 40-45 minutes you had best not be the only carry on your team.
I'm 10-2 with this hero, here are some example MatchID's of my play:
DP is so incredibly versatile you can play her with almost any gear. I generally get a cyclone stick so I can cyclone ultimate myself in the middle of the team. Bracers are also good because she is squishy. They can be upgraded later. I don't get nulls because her last hit is just so bad it's not really worth improving. I either get phases or travels for moves peed, chasing and push. Then either linkens or bloodstone. If the team has lots of nukes and stuns, linkens is better. Now it gets really fun. Endgame you can get shadow blue (for invisible ulti), heart for tankness, yasha for move speed, desolator (it stacks with your ulti), sheep stick. Shivas I never get but it's OK for more armor etc. I just think Shivas is better on a hero like tide than DP.
So you can see I aim to maximize speed, survivability and tankness with DP.
I wouldn't say that there is any consensus of her as high-tier, as very few professional games in the past month have included her as a pick or ban.
She is fairly tanky, and is often built even tankier due to the nature of her ult and the time you must survive to deal full damage and receive the heal. Her playstyle is similar to a necrolyte's, as you often build a bloodstone and use the high mana regen and low ability cooldowns to stand in the middle of a fight and continually cast. Usually she is not really built to solo kill or chase enemies, but to tank and cast a lot in a teamfight. Her nuke does fairly good damage, especially combined with the low cooldown afforded by witchcraft and the amount of casts you can get with a bloodstone's regen. The silence is also strong in fights, as a silence on an escaper(riki, QOP, storm) can allow kills when they cannot blink or ball lightning away. The silence on teamfighters can win a fight for you, especially if you can silence and kill a tidehunter or other guy with a big ultimate before they can cast it.
Her ultimate is useable for solo kills, but is is more commonly used to provide damage in an AOE over an entire teamfight, or to push a tower. Using your ultimate at a tower basically forces the other team to attack you or lose the tower, allowing you to force a teamfight. With team coordination, this can allow your team to get ready for a fight by getting in optimal position. Furthermore, keeping up with enemies should not be too difficult, as both the phase boots most death prophets get, as well as your witchcraft passive add to your movespeed. If it is a problem, a forcestaff could be built, or even better, a scythe of vyse to disable the opponent.