Is it okay to ask your research paper co-author (first place) to write a letter of recommendation for your PhD admission? I finished my school almost 10 years ago. Now, I have planned to go back to academics to pursue my Ph.D. Graduate schools usually ask Ph.D. candidates to get the recommendation letter from either your teacher or someone who supervised you in any past research project. In my case, I have no contact with any of my past professors. Also, my last highest degree (MS) was based on coursework (not research based) which means I never worked under any supervisor before. However, I have published some peer-reviewed research papers (as co-author) in collaboration with other researchers (working at different institutions). I would like to know if it is a good idea to ask one of my co-authors (first author) to write a letter of recommendation to support my Ph.D. application. Please suggest!
Yes, this is completely ok, even recommendable. You want your letter writers to know how you function in a research context. It does not matter if this was as part of a university research project (such as a thesis) or some other project that you worked in for some reason.

The main reason why most applicants use their former research advisors is because this is the primary way how undergrads get in touch with professors in a research (as opposed to a classroom) context.