Viruses rely on the host translation machinery to synthesize their own proteins. Consequently, they have evolved varied mechanisms to co-opt host translation for their survival. SARS-CoV-2 relies on a non-structural protein, NSP1, for shutting down host translation. Despite this, it is currently unknown how viral proteins and host factors critical for viral replication can escape a global shutdown of host translation. Here, using a novel FACS-based assay called MeTAFlow, we report a dose-dependent reduction in both nascent protein synthesis and mRNA abundance in cells expressing NSP1. We perform RNA-Seq and matched ribosome profiling experiments to identify gene-specific changes both at the mRNA expression and translation level. We discover a functionally-coherent subset of human genes preferentially translated in the context of NSP1 expression. These genes include the translation machinery components, RNA binding proteins, and others important for viral pathogenicity. Importantly, we also uncover potential mechanisms of preferential translation through the presence of shared sites for specific RNA binding proteins and a remarkable enrichment for 5' terminal oligo-pyrimidine tracts. Collectively, the present study suggests fine tuning of host gene expression and translation by NSP1 despite its global repressive effect on host protein synthesis.