How can an undergrad from a country with little 'international' research improve his chances of being a "good fit" for a top PhD program?
Ok, good question, but let's eliminate the phrase, "noting the difficulty/impossibility in doing any ground-breaking research especially as an undergraduate here?"  This actually applies to almost the entirety of the undergraduate population.  Very few undergraduates work on ground-breaking research projects -- and, if they do, their role on the actual project is unlikely to be the intellectual driver.  They might have done some lower-level work under the supervision of the principal investigator (PI).

So, your question is really about how to improve your chances of acceptance in general.  That really depends on the discipline, and it really depends on the program to which you are applying.  Every program has a unique admissions committee that will review applications and assign different levels / weights to factors they consider important in making admissions decisions.  Thus, certain programs may place a lot more emphasis on GRE than other programs.  Some programs might consider letters of recommendations to be very important, which other programs may consider letters of recommendation to be of little importance (since most letters of recommendations are cherry picked from the possible letter writers).  

That said, your task is to tailor every application to the programs where you are submitting an application.  A general snowball approach where you submit the same application everywhere is an alternative strategy, but one that I advise against.  Learn what those programs value most in their admissions decisions, and tailor the application accordingly.  Of course, it is hard to figure out what they value, so you have to do a lot of researching -- e.g., any published data on the current and previous cohorts?  

Good luck!