Bacteriophages are ubiquitous in nature and represent a vast repository of genetic diversity, which is driven by the endless coevolution cycle with a diversified group of bacterial hosts. Studying phage-host interactions is important to gain novel insights into their dynamic adaptation. In this study, we isolated 12 phages infecting species of the Acinetobacter baumannii-Acinetobacter calcoaceticus complex which exhibited a narrow host range and similar morphological features (podoviruses with short tails of 9–12 nm and isometric heads of 50–60 nm). Notably, the alignment of the newly sequenced phage genomes (40–41 kb of DNA length) and all Acinetobacter podoviruses deposited in Genbank has shown high synteny, regardless of the date and source of isolation that spans from America to Europe and Asia. Interestingly, the C-terminal pectate lyase domain of these phage tail fibres is often the only difference found among these viral genomes, demonstrating a very specific genomic variation during the course of their evolution. We proved that the pectate lyase domain is responsible for phage depolymerase activity and binding to specific Acinetobacter bacterial capsules. We discuss how this mechanism of phage-host co-evolution impacts the tail specificity apparatus of Acinetobacter podoviruses.