Of the three Rogue/DPS matches, this one can be the easier or hardest depending on their gear. Like the Lock/Rogue, they will try to Fear you in order to do their gib combo of Blind/Sap/Silence/Fear. The key difference the Lock can cast fear, while the priest Fear is limited to range, so it's much easier to avoid. This match can be longer than the Rogue/Warlock combo, as the Priest can heal, so you won't be able to simply kill one quickly, but Shadow Priests run themselves OOM really fast, so just outlast his mana pool for a win. Keeping Hamstring on the both the Priest and Rogue is very important, it allows you to kite them much easier. The big danger in this match is the Priest chain dispelling your HoTs while the Rogue goes to town on you/your Warrior, so don't ever give them a chance to do so, always try to keep your Warrior up. He needs to be very very watchful of his own health, and back off and play defensive if you're to busy to get a HOT on him if the Rogue is on you.
They will likely have their Priest mounted at the start while the Rogue goes hunting for you.
You cannot afford to play aggressive here. Spriest/Rogue can melt your Warrior very very quickly, catching him in 2her/zerk with a Kidney, or even a Blackout, can result in him dying regardless of what you do.
So, you both need to be very aware of WHAT they're doing, is you get away from their Rogue, don't run blindly, that Rogue is going to turn on your Warrior and melt him while you're far away.
The whole idea here is to simply be running and turtling, running their Priest OOM. The ideal situation you two can be in here is that you both are running AWAY from them, with them Hamstrung behind you while the HoTs are ticking your Warrior to full.
Only send your Warrior back in if he's hotted/high on life.

They will do one of three tactics: on your Warrior, on you, or split DPS.

They're on your Warrior:

If the Rogue pops out on your Warrior, have your Warrior Hamstring him as well as the Priest. When the Warrior gets low (75%), make sure you're as far away from the priest as possible, then Pop out (Abolish/HoT yourself first if the Rogue hasn't popped yet), and Abolish him first to get rid of the poisons, then proceed to hot him up. Make sure to stay at max range as you do this so you have some breathing room distance wise, and it gives your Warrior an escape option with Intervene.

The Rogue will likely continue to DPS the Warrior while the Priest starts running for you to Fear you, but as long as you keep the Priest Hamstrung you should be able to run and keep HoTs/Abolish up without getting feared. If the Rogue pops sprint and starts running towards you, he's trying to Blind you so the Priest can fear you. Have your Warrior do his best to Intercept and re-Hamstring the Rogue so he doesn't get that Blind off. (or he can Intervene to eat the Blind for you). If the Rogue Blinds you, have your Warrior put on a shield and start LOSing/Spell Reflecting, but DON'T TRINKET IT UNLESS THE WARRIOR IS LOW. The Rogue will usually keep you locked up after the Blind in case you trinket, while the Priest gets close enough to Fear you. If you trinket blind, then eat a Silence/Cheapshot/Kidney Shot/Gouge/ into the fear, etc, then your Warrior is probably ganna die. So, save your trinket for the follow up Fear or Sap.

If he's not out of mana from trying to DPS you already, the priest will drop out to start healing if one of them gets low. Shadow Priests have no mana efficiency, so the game is pretty much over at this point. Stay at max range, keep abolish poison up, and eventually one of them will die or the priest will go oom.

Your Warrior needs to be very quick to shield up. If he's under 70%, he has a shield on. He will likely spend most of this match with a shield on, so don't be to afraid to do so. The priest will run himself OOM very quickly, so just outlast his mana. If he gets low, he needs to intervene to you, and you both then run away from them until his hots catch him back up, where he then runs back in to re-hamstring and land a couple blows on the rogue before he shields back up.

If they're on you:If they open up and try to kill you, have your Warrior sit on their Rogue. Between Intercept stun/mace stun/disarm/imp hamstring, the Rogue won't be able to do much damage, and the Priest can't do enough damage when you're pillar kiting to kill you, so as long as you keep the wound poisons down with abolish and the hots up, you should be able to kite them around until your Warrior forces their Priest out to heal. When the Priest goes holy, it's a bad HPriest/Rogue combo, which you dominate.

Splitting DPS:This is generally considered the "hardest" team. Here, your Warrior is supporting you the best he can, but with a shield on. The Priest will solo the Warrior until you come out, and the Rogue will jump you then. They will split DPS, with the Priest on the Warrior and the Rogue on you until one of you gets low, then they will switch to go for a kill on one of you. This fight you will likely not gain a kill fast, so what we do is have the Warrior sit in defensive stance and spam Hamstring on the Rogue(Proc mace stun/Imp Hamstring), and like the Mage/Rogue fight, just outlast the Rogue's cooldowns.

The Warrior will be taking damage from the Priest, but as long as he has a shield/reflecting/Defensive stance he should be durable enough to take a beating while he supports you so you can get away, where he will them Intervene you so you can both escape them.

The ultimate goal in this fight is to get to the point where you both are running AWAY from them, with them Hamstrung behind you while your HoTs are ticking you both back to full so he can go back in. Outlast the Rogue's cooldowns until he's out of tricks. When the Rogue is completely spent, then you can start playing offensively. Any sooner, and your Warrior is risking being caught in a Kidney Shot with a two hander in berserker, and being bursted down while the Priest slams dispel purging your abolishes and HoTs.

Notes:

• Again, Shadow sight to avoid the blind/saps. It's amazing when they blind you and it insta breaks.
• When the Shadowfiend pops, have the Warrior go shield while you cheetah around kiting it. Don't let that thing hit you if you can avoid it, every hit prolongs the match.
• Some priests will try to mana burn you. As long as you stay out of max range, you should be fine. If they attempt to have the Rogue on you while the Priest mana burns, have your Warrior on the Priest, because if the Priest is just mana burning he's not trying to do damage, and you can get away from a rogue with an occasional Intervene/Hamstring/Disarm from your Warrior
• Watch the Dispels from the Priest. Dispelling abolish poison can lead to stacking of wound, which is very, very bad. Keep abolish up, cover it with lifeblooms/rejuvs(both rank 1 and full rank), etc.
• Intervene will absorb blind. It's usually very, very obvious when the rogue is going to blind you, so if your warrior can do a quick intervene on you when he sees the rogue start sprinting towards you, it'll stop you from getting blinded.