We study the heavy quark mass (m_h) dependence of observables built from heavy-light meson correlation functions in small-volume lattice QCD after taking the continuum limit. In this setup we are able to enter the asymptotic mass-scaling regime as 1/m_h -> 0 and to perform well-controlled extrapolations to the infinite-mass limit. Our results are then compared to predictions obtained in the static limit of continuum Heavy Quark Effective Theory (HQET), in order to verify non-perturbatively that HQET is an effective theory of QCD. While in general we observe a nice agreement at the per cent level, we find it to be less convincing for the small-volume pseudoscalar decay constant when perturbative matching is involved.