It was on The Dorsey Brothers Stage Show at the CBS studio in New York. Elvis played just two songs: "Shake Rattle and Roll" and "I Got a Woman". The show was just was directed by Jackie Gleason and was only 30 minutes of random music acts as a warm up for "The Honneymooners" that started at 8:30.
At that time Elvis was not so well known in New York, but there was a stir and then 30 seconds into the act. According to www.elvis.com.au ("one serviceman stationed in New Jersey in attendance that evening said, 'I often went on Saturday nights to the Dorsey brothers show and I was there when Elvis Presley made his national television debut on that show. I had never heard of him and was startled when he appeared on stage and hundreds of girls began screaming'.")
Compare the first act of the Stage Show with Elvis' act in crowd participation and style. You can see how music changed the face of televison.
I never got much into Elvis, but if I knew this younger Elvis I probably would have.