> The question is, when they offer me with a lower rate how should I deal with the situation so that I don't loose the position and get away with the best deal?
There are no guarantees in negotiation. Projecting confidence and being willing to walk away from a lowball offer will help you negotiate.
If you give the impression that you have no other options and that you will be taking the job even at the lower price, they will likely offer the lower price.
If you give the impression that you are not interested in the job unless they accept your higher price, they will be more likely to negotiate. However, they might also look for alternate candidates who are willing to accept the lower rate. This is a risk you must accept.
One of the best things you can do for yourself is to continue searching for other jobs until you have accepted an offer. Getting too attached to any one job will diminish your negotiating position and the other side may sense this. There will always be more job offers, so don’t sacrifice your requests just to take the first one.