Assisting an acquaintance with a simulation where a very large number of binomial probability calculations are required, I pointed them to a slightly obscure function to dramatically speed up their algorithm. Specifically, for
Probability[x == b, x \[Distributed] BinomialDistribution[n, p]]
the same result can be had with
BernsteinBasis[n, b, p]
but the latter is 15-20X faster (and surprisingly generally more accurate with inexact p) than the former, and 1.5-2X faster than PDF calculation. Only explicit calculation using the formula for binomial probability is faster.
I'm curious what other "off-label" uses of built-in functions have been noted to have performance advantages.