If the machine in question has the pax utility, you can use its -s option to manipulate the path that gets stored (and even strip it completely, leaving just each file's basename). The POSIX man page is here (your implementation may differ, but it probably won't matter for simple stuff):
http://www.opengroup.org/onlinepubs/009695399/utilities/pax.html
The "tar -C" thing will get the job done in this case, but pax is more powerful, and thus worth knowing about, IMO.