Can a professor influence the graduate admissions committee if he or she is interested in a particular student? I've had a promising Skype interview with a great professor from a top-level university in US. Our research interests are closely related and he encouraged me to apply BUT he says that all decisions are finally made by admission committee there.

The question is "Is a professor in such a high-level university able to affect admission committee if he really wants a student?" or "Does admission committee decision-making process become easier if a professor really wants an applicant?"

The main point is the difference between my transcript (which is a real catastrophe!) and my research background which is pretty good so the professor's decision might be different from admission committee.
Being on the graduate committee of my department, if a professor sends us a note that they'd like to have a student admitted and state that they will take on their adviser role, we will only not admit that student if there are any red flags in the file. Most other considerations (including GPA) are not all that important any more at that point.

The reason for this is that what you get to see about a student from their application file is really just a very inexact science. You get transcripts that don't say very much about the standards in each of the classes a student took, letters of recommendation that sound the same for almost all students, and statements of purpose that most of the time are pretty generic as well. In my assessment of files, GRE scores and the statement of purpose often carry most of the weight, but I am fully aware of the fact that GRE scores poorly correlate with success in graduate programs. In other words, if I can get a personal opinion from one of my colleagues stating that they're excited to work with a student, then that is worth a whole lot and it will carry the day unless there are obvious reasons in the file of a student to reject the application.