I understand where you are coming from. I used to have the same problem. To overcome this takes a concerted effort and dedicated practice.
You must develop muscle memory so that you can put your brain and fretting hand on auto pilot. To internalize the movements needed to play a song, take one part at a time. Play it over and over while looking at the fret board and be sure you are able to play it comfortably and smoothly with no mistakes.
Then try playing it with your eyes closed or in a dark room. At first you will miss some notes or barre chord positions. Keep practicing over and over - one section at a time until you can play the song in the dark.
It was a big help for me to learn to play without looking at the fret board. Not only can I make eye contact with my audience, but I don't have to worry about if dim stage lighting will not let me see the fret markers.
I recommend playing a section over and over while looking - and then try to play it with your eyes closed or just looking at something other than your guitar neck. Then if you mess up you can open your eyes and see what you are doing wrong and make the needed adjustment.
Once you are able to play the whole song with your eyes closed, try it in a dark room so you don't even have the option to open your eyes. Once you are able to play the song in pitch black darkness, you have it - and will never need to look at the fret board again for that song.
EDIT: Your brain will lock in to the positions on the fret board instinctively with enough practice. To prove this, close your eyes and touch the tip of your nose. Try your ear lobe. These are things your brain locked into when you were a baby. Or another example - most folks can find the snooze button on their alarm clock while half asleep without turning on the light or even opening their eyes.
I find that I unconsciously touch base with where the headstock joins the neck as a frame of reference from time to time to get my bearings (similar to placing your first fingers on the home keys on your keyboard before touch typing). You can feel that spot on the neck because there is an change in the angle and also can feel the nut with your first finger.
One final tip. Some folks will put stick-on round labels (dots) on certain reference points on the back of the neck so they can feel them as they slide their hand up and down the neck. The larger ones stick better. Don't do this on a vintage guitar - but if you play your work horse guitar on stage - give it a shot.