You can increase horsepower either of two ways:

1) More air and more fuel
2) Reduction in parasitic loss

The idea behind an air filter that flows more easily is that at light load where you're throttling the amount of air going into the engine anyway, it reduces the parasitic loss of having to suck air through a filter. When you reduce parasitic losses, you're not increasing fuel usage at all. In fact, if you get more power from the same amount of fuel, that means you will achieve cruising speed more quickly, at which point you throttle back to your normal cruising power setting.

If you wanted to read more about the science of making horsepower, try doing a search on BSFC and getting a full understanding of what that means and how you would put it to use in the real world.