We match continuum and lattice heavy-light four-fermion operators at one loop in perturbation theory. For the heavy quarks we use nonrelativistic QCD and for the massless light quarks the highly improved staggered quark action. We include the full set of ΔB=2 operators relevant to neutral B mixing both within and beyond the standard model and match through order αs, ΛQCD/Mb, and αs/(aMb).