What you describe is "point shooting" which is usually a developed trait. There are books on the subject and probably Internet sites as well. If you already have a natural point ability, avoid those books and websites as they may instil a mental block over your natural ability.
Point shooting is the reason that, when purchasing a firearm, one needs to establish the "natural point" of the firearm. This is done, with a handgun, by taking your normal stance, fixing on a target, closing your eyes, and then bringing the firearm up to where you feel that it is pointed at the target previously established. Then open your eyes.
You should, if the firearm is correct for your "natural point", be looking straight over the top of the backstrap and the sights should be on the target. If the firearm is pointing down, up, right, or left, try the excercise again. This should be done 6-10 times to establish the natural point of the firearm. The best firearm, with the most natural point for me, is a Browning Hi-Power. When I perform the excercise with this firearm, I am looking right over the sights with rare exception.