Take another look at the original sentence:
You wanted to fix it this way:
To add a comma between pencil and finally would create an equally bad problem, a comma splice. A comma splice occurs when you have two main clauses joined with a comma alone. Jayson started poking Kim with the sharp tip of his pencil is the first main clause. Finally she whirled around and slugged him in the mouth is the second main clause. The spot between pencil and finally needs a stronger break than a wimpy comma.
You might want to consult the rules for fixing comma splices and fused sentences.