The coronavirus disease 2019 pandemic, caused by the novel severe acute respiratory syndrome coronavirus 2 (SARS-CoV-2), is an ongoing global health threat with more than two million infected people since its emergence in late 2019. Detailed knowledge of the molecular biology of the infection is indispensable for understanding of the viral replication, host responses, and disease progression. We provide gene expression profiles of SARS-CoV and SARS-CoV-2 infections in three human cell lines (H1299, Caco-2 and Calu-3 cells), using bulk and single-cell transcriptomics. Small RNA profiling showed strong expression of the immunity and inflammation-associated microRNA miRNA-155 upon infection with both viruses. SARS-CoV-2 elicited approximately two-fold higher stimulation of the interferon response compared to SARS-CoV in the permissive human epithelial cell line Calu-3, and induction of cytokines such as CXCL10 or IL6. Single cell RNA sequencing data showed that canonical interferon stimulated genes such as IFIT2 or OAS2 were broadly induced, whereas interferon beta (IFNB1) and lambda (IFNL1-4) were expressed only in a subset of infected cells. In addition, temporal resolution of transcriptional responses suggested interferon regulatory factors (IRFs) activities precede that of nuclear factor-κB (NF-κB). Lastly, we identified heat shock protein 90 (HSP90) as a protein relevant for the infection. Inhibition of the HSP90 charperone activity by Tanespimycin/17-N-allylamino-17-demethoxygeldanamycin (17-AAG) resulted in a reduction of viral replication, and of TNF and IL1B mRNA levels. In summary, our study established in vitro cell culture models to study SARS-CoV-2 infection and identified HSP90 protein as potential drug target for therapeutic intervention of SARS-CoV-2 infection.