Ballet dancer Kathryn Morgan recommends this tip: when gearing up for a big performance, practice running the piece twice in a row.
In the blur of performance, it can be easy to forget that the body is in fact more physically stressed onstage than it is in a practice room. Studies have shown that musicians display elevated blood pressure, increased muscle tension, and faster breathing rates while in performance. After experiencing these physical stressors for a sustained period, we may resort to harmful habits (such as straining to get a bigger sound) simply because we're too energy-depleted to be mindful about what we're doing.
For example, I often feel jittery at the beginning of a performance, but it's toward the end that I tend to make mistakes. It's a trade-off: 40 minutes into a long concert I may feel totally at ease – yet this ease results from having physically tired myself out, a state that can impair my mental focus.
If you can, practice-performing a piece or program twice consecutively is a good way to develop the physical and mental stamina to combat onstage fatigue. If you can do it twice in a practice room, you'll certainly be able to do it once in performance!