Mentioning unpublished research paper in Statement of Purpose/Resume I graduated two years ago with a BE degree. At that time, I did not have any plans for Ph.D./higher education, so I did not put any effort to publish my undergrad research work in any conference. 

Now things have changed a lot, and I am applying to Ph.D. programs. To strengthen my research profile, I have entirely reviewed my undergrad dissertation, and manage to come up with a research paper out of it.

The problem is that there is no time to publish this paper as the paper submission date of a potential conference will open up next year, and my grad applications are due next month. 

I wanted to know how I can mention my unpublished research paper in my Statement of Purpose, Resume? Considering that the research paper is highly relevant to the Ph.D. program I am applying to.

(Do I also need to mention the reason behind publishing my research work so late? like after two years)
You can certainly mention "work in progress" or "submitted, not yet accepted" and the like in your materials. Just label things for what they are. Two years isn't really a long time for research in most fields, so I wouldn't worry much about the time. It is also natural, if you have been working in the field to immerse yourself in that for a while. 

But submitting the work is marginally better than not.