At lvl 73, you cannot really sustain healing that pull as a holy priest; and as you level up it will only get worse due to the constanly decreasing spirit regen. Not until you hit some heroic gear will you comfortably be able to heal it.
That's not to say it's impossible. It's just hard.
* The best way to make your tank to use the lightwell. It's healing for a hell of a lot, and unless the tank is severely undergeared, incoming damage won't break the effect. By using the lightwell, the tank will remedy your mana issues, but the workload is now on him.
* Get a better geared tank. Having a damage spunge tank will be a lot harder than a tank dodging 80% of the blows.
* A druid giving you innervate will be your best friend until you get some heroic gear. Bring one!
* Bring a lot of mana potions. You will need them!
* Consider getting some of the dark runes. Every little ounce of mana helps
* Keep Prayer of Mending bouncing. This is the hard part, but if it bounce a lot it's your most mana efficient heal after the lightwell. Learning to use it well is vital for surviving the time until you get heroic gear.
* Get someone with replenishment. It makes a lot of difference.
* Flash Heal is too expensive. It's a staple spell at raiding, but until you get heroic gear, spamming it is no option as you likely won't even have replenishment. Use it, but hold back as much as possible. Don't use it on the tank, ever. Make sure that you always trigger Serendipity if you do use it.
* Same problem with greater heal. They say it's more efficient, but it's not that much more efficient. Casting one will hurt your manapool severely. Use it, but hold back when possible. Try to trigger Serendipity AND Test of Faith for the best effect. Doing so is a timing-critical job, but without both procs, you are not maximizing the use of your build.
* Renew is more expensive than a flash heal, effectively heals for less and slower and doesn't proc Holy Concentration or Surge of Light. Don't use it, ever. Reconsider that stance in 3.1.
* Consider respeccing Discipline. Holy is a horribly mana-inefficient healer which doesn't work without lots of support from other classes. Discipline has infinite mana until 3.1 hits us and while bringing weaker heals to the table can still hold his own much more reliably than holy.
* If you are very pressed for mana, stand in a cleave. The 15 extra healing in angelform seconds will be the last thing you do you, but it usually saves the tank. If you have a warlock, get a soulstone before doing that. Either way, expect to run a lot.
* Call for assistance! A shadowpriest, shaman, boomkin, cat or retardin can all help you with the healing. For this pull, it's not a sign of weakness to require assistance.
* Use a bandage. You are desperate after all.
* Give your tank and party some healing potions. This will save you a quarter of a manabar. Warlock soulstones are of equal value.