I obtained a Masters Degree from a U.S. university, but my graduate school major was not related to the job offer. My employer will file an H-1B petition based on my bachelor's Degree major. Can I use the additional 20,000 H-1B visas for advanced degree professionals?

Yes. As long as you have obtained an advanced degree in the U.S., you can use the additional 20,000 H-1B visas for advanced degree professionals.