The repertoire of currently available antiviral drugs spans therapeutic applications against a number of important human pathogens distributed worldwide. These include cases of the pandemic severe acute respiratory coronavirus type 2 (SARS-CoV-2 or COVID-19), human immunodeficiency virus type 1 (HIV-1 or AIDS), and the pregnancy- and posttransplant-relevant human cytomegalovirus (HCMV). In almost all cases, approved therapies are based on direct-acting antivirals (DAAs), but their benefit, particularly in long-term applications, is often limited by the induction of viral drug resistance or side effects. These issues might be addressed by the additional use of host-directed antivirals (HDAs). As a strong input from long-term experiences with cancer therapies, host protein kinases may serve as HDA targets of mechanistically new antiviral drugs. The study demonstrates such a novel antiviral strategy by targeting the major virus-supportive host kinase CDK7. Importantly, this strategy focuses on highly selective, 3D structure-derived CDK7 inhibitors carrying a warhead moiety that mediates covalent target binding. In summary, the main experimental findings of this study are as follows: (1) the in vitro verification of CDK7 inhibition and selectivity that confirms the warhead covalent-binding principle (by CDK-specific kinase assays), (2) the highly pronounced antiviral efficacies of the hit compounds (in cultured cell-based infection models) with half-maximal effective concentrations that reach down to picomolar levels, (3) a particularly strong potency of compounds against strains and reporter-expressing recombinants of HCMV (using infection assays in primary human fibroblasts), (4) additional activity against further herpesviruses such as animal CMVs and VZV, (5) unique mechanistic properties that include an immediate block of HCMV replication directed early (determined by Western blot detection of viral marker proteins), (6) a substantial drug synergism in combination with MBV (measured by a Loewe additivity fixed-dose assay), and (7) a strong sensitivity of clinically relevant HCMV mutants carrying MBV or ganciclovir resistance markers. Combined, the data highlight the huge developmental potential of this host-directed antiviral targeting concept utilizing covalently binding CDK7 inhibitors.