You know, when you said name the TV commercial, I had a feeling it would be this tune, before I even played it.
The song is called "No Matter What Shape (Your Stomach's In)" and was originally done by the group The T-Bones (hit 45 on Liberty Records, entered most charts in Dec. 1965, was a hit through early 1966).
But this version you have here is not The T-Bones. It sounds close to the original, but even the first drum beat told me it's someone else. The info that appears at the top of the screen while it's playing says Spooky Pie. Could that be the name of some new band that covered the song? Whoever it is did a good job, but it's not the original hit version by The T-Bones.
The TV commercial it was used in was for Alka-Seltzer. In fact, the front cover of the T-Bones' 1966 album featuring the song is a montage of images from the commercials, showing various shaped stomachs.