I'm not certain it was Murrow who primarily beat McCarthy:
Al Gore, Edward R. Murrow and Senator McCarthy
But the advent of TV journalism led by CBS changed things IMO. TV catered more to the masses and the lefties there were able to demogogue through appearance and pictures. I believe McCarthy began to lose his steam when Murrow took him on because it was impossible for McCarthy to compete with the "glamour" of TV.
Sort of the same principle by which many say Nixon lost his debate with Kennedy because he didn't appear have to same movie-star qualities on TV (however, many of those who heard the debate on the radio thought Nixon had won).