The measles virus and rubella virus are two separate viruses. They have different DNA and RNA structures, and the vaccination for the measles virus only "knows" how to attach itself to measles and destroy the virus. It doesn't know how to attach itself to the rubella virus to destroy it, as the vaccination is needed to inform it how to.
The advantage of vaccinating a large amount of the population is that it reduces the chance someone will catch sickness by a great amount, and can possibly eradicate the virus.