the best way is to run, lol
other than that. Get a linken's sphere, that should stop the first mana burn attack. It nullifies one magical attack every 60 seconds or so.
A Mana Mek works fine too. Only costs 25 mana to cast and it will replenish your mana pool and that of your friends. Cool down is pretty short.
If all else fails, build a necromicon book. Do unto others as they do unto you. The book creates creeps that mana burn pretty intensely.
Sic' em boys!
www.dotaportal.com has tons of strategies too, if you want to go real hard core.