This idiom or expression has to do with:

Getting out of a bad legal situation without being punished.

A. Didn’t they arrest him for stealing from his mother?!
B. Yeah, but somehow he beat the rap and avoided going to jail!!

Also see:
Get away with something.

This idiom or expression has to do with:

Doing something wrong and not getting caught.
Doing something wrong and, if caught, not getting punished for it.

A. Did they ever catch the guy who stole your watch?
B. No, he got away with it!!
A. But they caught the guy who stole your bike, right?
B. Yes, but he got away with it, too. I guess he was good at explaining things!!

Also, related:
Getting away with murder!!

If someone says “Jerry can get away with murder,” they mean something like “He’s extremely good at explaining things!”

Also see:
Beat a rap.