Human cytomegalovirus (CMV) is a ubiquitously distributed pathogen whose rodent counterparts such as mouse and rat CMV serve as common infection models. Here, we conducted global proteome profiling of rat CMV‐infected cells and uncovered a pronounced loss of the transcription factor STAT2, which is crucial for antiviral interferon signalling. Via deletion mutagenesis, we found that the viral protein E27 is required for CMV‐induced STAT2 depletion. Cellular and in vitro analyses showed that E27 exploits host‐cell Cullin4‐RING ubiquitin ligase (CRL4) complexes to induce poly‐ubiquitylation and proteasomal degradation of STAT2. Cryo‐electron microscopy revealed how E27 mimics molecular surface properties of cellular CRL4 substrate receptors called DCAFs (DDB1‐ and Cullin4‐associated factors), thereby displacing them from the catalytic core of CRL4. Moreover, structural analyses showed that E27 recruits STAT2 through a bipartite binding interface, which partially overlaps with the IRF9 binding site. Structure‐based mutations in M27, the murine CMV homologue of E27, impair the interferon‐suppressing capacity and virus replication in mouse models, supporting the conserved importance of DCAF mimicry for CMV immune evasion.