Home Ownership Can Suck

It's been pissing rain for three days now. I have just discovered that my roof has a leak around the furnace exhaust pipe. The shingles are only a few years old, but the exhaust pipe is original; about 35 years old. I just got back from the roof (in the rain) and the shingling around the pipe looks good. I'm guessing that one of the seams of the pipe has rusted through.

Crap.

Updated 3/9: Yesterday I checked out the roof. The tar that is supposed to seal the nailholes in the pipeflange is all old and cracked. It is 35 years old. So, I chipped off what was left of it and re-tarred all the nails for all the pipes.
I also noticed that the fly-by-night roofers I had hired a few years ago did a piss-poor job on sealing the nailholes in the peak vent that they installed. Since I was already up there, I covered all of them as well. Hopefully, that will do it.