The sentence in which a comma is used correctly is:
A. In the first round of the tournament, I played one of the best teams.
A comma is placed right after a subordinate clause. A subordinate clause is not a complete sentence and they need to be accompanied by an independent clause (can stand on it's own), in order to form a complete thought.
Here is where the comma should have gone in order for options b and c to be correct:
b. In the first round of the tournament, I played one of the best teams.
c. Fortunately, I had a spare set of keys with me.