The sentence in which a comma is used correctly is:
A. <em>In the first round of the tournament,</em> <u>I played one of the best teams. </u>
A comma is placed right after a subordinate clause. A <em>subordinate clause</em> is not a complete sentence and they need to be accompanied by an <u>independent clause</u> (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. <em>In the first round of the tournament</em>, <u>I played one of the best teams. </u>
c. <em>Fortunately</em>, <u>I had a spare set of keys with me.</u>