Herpesvirus infection initiates a range of perturbations in the host cell, which remain poorly understood at the level of individual cells. Here, we quantify the transcriptome of single human primary fibroblasts during the first hours of lytic infection with HSV-1. By applying a generalizable analysis scheme, we define a precise temporal order of early viral gene expression and propose a set-wise emergence of viral genes. We identify host cell genes and pathways relevant for infection by combining three different computational approaches: gene and pathway overdispersion analysis, prediction of cell-state transition probabilities, as well as future cell states. One transcriptional program, which correlates with increased resistance to infection, implicates the transcription factor NRF2. Consequently, Bardoxolone methyl and Sulforaphane, two known NRF2 agonists, impair virus production, suggesting that NRF2 activation restricts viral infection. Our study provides insights into early stages of HSV-1 infection and serves as a general blueprint for the investigation of heterogeneous cell states in virus infection.