We show that quasi-alternating links arise naturally when considering surgery
on a strongly invertible L-space knot (that is, a knot that yields an L-space
for some Dehn surgery). In particular, we show that for many known classes of
L-space knots, every sufficiently large surgery may be realized as the two-fold
branched cover of a quasi-alternating link. Consequently, there is considerable
overlap between L-spaces obtained by surgery on $S^3$, and L-spaces resulting
as two-fold branched covers of quasi-alternating links. By adapting this
approach to certain Seifert fibered spaces, it is possible to give an iterative
construction for quasi-alternating Montesinos links.