A few thoughts on messing up.
First, if a piece has been thoroughly practiced so that it is firmly in the mind and in the fingers, messing up should be less likely. If you truly know it, you ought to be able to perform it without mishaps.
Second, in performance you have to be concentrating only in the moment, focusing on the technical points, emphases, pedal effect, etc. in that measure alone. If you start thinking too far ahead, i.e., anticipating approaching a difficult spot, three things are happening: 1) you're trying to play what you're playing, 2) you're anticipating and worrying about something to come, and 3) the rattling noise of fear is entering your brain. Once the mind trifurcates like that it's disaster time. You'll mess up what you're doing in the moment, plus that mess-up will be the lead-in to the really tough spot you anticipated causing articulation there to fall apart as well. Don't let your thoughts get too far ahead of what you're actually doing.
In performance do with your eyes what you always do in practice. If you play the entire piece with your eyes closed, do it. If your are like the late George Bolet and your eyes are constantly glued to the keyboard, then stay glued in performance. If you do a mix, for example, look straight ahead during an extended lyrical part, but then look down at the keyboard at your weaker hand when both hands must execute a wide leap, do it. Don't vary anything in performance. The point here is that if your habit is to look into the stage wing, but you have a sudden curious urge to see what your hands are doing, and you're mind-eye coordination is then in an unfamiliar place, here comes the mess-up again. Gain those interesting perspectives at home, not on stage.
Finally, bear in mind that it's been proven over and over again that nervousness can make you perform in public at a faster tempo than normal, even though you're not conscious of it. Don't allow it! Sit there and calmly contemplate your real tempo in starting the piece and maintain it throughout. A faster tempo is unfamiliar territory, more demanding, higher risk, and can lead to fumbling.