How were the Americans able to defeat the Japanese when they appeared to be at such a disadvantage?

Are you talking just about the Battle of Midway, which
you've tagged it with?

If so, I have two answers.  First, I
do not think the US was at as much of a disadvantage as your question suggests.  The
number of airplanes available to both sides was not that different, I believe.  The
Zeroes were much superior to American fighters, but the other airplanes were not all
that different.

Secondly, the US had a great deal of luck. 
They managed to catch the Japanese in the middle of trying to switch types of weaponry
on their aircraft and trying to refuel.  This meant that the Japanese carriers were very
vulnerable to attack.