  We develop the theory of quasi-$F$-splittings in the context of birational
geometry. Amongst other things, we obtain results on liftability of sections
and establish a criterion for whether a scheme is quasi-$F$-split employing the
higher Cartier operator. As one of the applications of our theory, we prove
that three-dimensional klt singularities in large characteristic are
quasi-$F$-split, and so, in particular, they lift modulo $p^2$.
