Flights from Lima to Brazil can be pricey. I have done this route a couple times and was always surprised with how expensive it was. It is the most expensive flight I did in south america and I have done a lot of them.
It is normally cheaper to fly Lima to Sao Paulo then to flight Lima to RIO. Not sure which one you wanted but if you are flexible check both. Sometimes you can find better deals into Brasilia.

You should be able to find 17.5k legs from SFO to lima unless its in June, July or August. As someone else said it can even get down to 15k but its rare.

For in peru flights check peruvian airlines and Star peru. There is a few more cheap ones as well if you want to go off the gringo trail in Peru I can give some suggestions. Lan once in awhile has good deals in Peru but the normal cheap flights with LAN are for Peruvian residence only.

A tip for LAN is to check the prices on the peru site instead of the english site. It definitely can make a difference. If it does say the resident rule for the lowest prices I don't recommend buying it. Some people have had success but its very YMMV

If you have any questions about travel in Peru feel free to PM me. I lived there for 2 years and have traveled all over the country