Spray 'n Pray is fantastic for that mission: the explosive property takes down groups of mole rats with ease, and since it's a silenced weapon it doesn't usually alert rats that aren't close by.
Mines help a ton too- obviously when they burrow and pop up they go right under the mines, but if you can find areas that are steel flooring (staircases for example) the rats can't come up through that- which means they have to come up nearby and rush at you. Planting a few mines at the edge of the dirt areas means they pop up right into a high-explosive greeting.
Also, power armor is important- if you have power armor on, the first bite won't have the poisoning effect, only the second one. So while it's not foolproof, it DOES give you one mulligan at least. (Stealth Boy armor helps too, keeps the number of rats aware of your presence to a minimum).
That mission is a bitch- on this second playthrough I've actively been avoiding it just because it's such a beast. But... I hit level 81 earlier today, so it's probably time to suck it up and get started. Times like this, I miss Moira's glowing stick from Megaton...