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. However, 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 that a functionally-coherent subset of human genes are 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 uncovered a remarkable enrichment of 5′ terminal oligo-pyrimidine (TOP) tracts among preferentially translated genes. Using reporter assays, we validated that 5' UTRs from TOP transcripts can drive preferential expression in the presence of Nsp1. Finally, we found that LARP1, a key effector protein in the mTOR pathway may contribute to preferential translation of TOP transcripts in response to Nsp1 expression.Collectively, our study suggests fine tuning of host gene expression and translation by Nsp1 despite its global repressive effect on host protein synthesis.