Since your lease should have had language about the landlord's responsibilities for maintenance and I doubt they can expect you to repair the water heater this would be their liability.
It would be different if you were negligent or in breach of your lease (like if you left your tub running with the drain stopped for a day or so) but this doesn't sound like it.
You might want to contact your insurance carrier to see if the want to pay the liabilty claim and subrogate against the landlord. Sometimes they will do that and a lot of insurance attorney's really enjoy it.

