Welcome To The Hellmouth (1) - S1-E1
Revealing mistake: When Buffy sneaks into the locker room and checks out the dead body, you can see part of the outline around the prosthetic vampire bite on his neck (it isn't quite blended in properly), revealing it's an appliance.
Answer: She has superpowers, ergo fast movement. The reason she outruns him so easily in "Touched" is that she stops trying to actually fight him and just dodges instead.
Shay