Influenza A virus (IAV) enters host cells by endocytosis followed by acid-activated penetration from late endosomes (LEs). Using siRNA silencing, we found that histone deacetylase 8 (HDAC8), a cytoplasmic enzyme, efficiently promoted productive entry of IAV into tissue culture cells, whereas HDAC1 suppressed it. HDAC8 enhanced endocytosis, acidification, and penetration of the incoming virus. In contrast, HDAC1 inhibited acidification and penetration. The effects were connected with dramatic alterations in the organization of the microtubule system, and, as a consequence, a change in the behavior of LEs and lysosomes (LYs). Depletion of HDAC8 caused loss of centrosome-associated microtubules and loss of directed centripetal movement of LEs, dispersing LE/LYs to the cell periphery. For HDAC1, the picture was the opposite. To explain these changes, centrosome cohesion emerged as the critical factor. Depletion of HDAC8 caused centrosome splitting, which could also be induced by depleting a centriole-linker protein, rootletin. In both cases, IAV infection was inhibited. HDAC1 depletion reduced the splitting of centrosomes, and enhanced infection. The longer the distance between centrosomes, the lower the level of infection. HDAC8 depletion was also found to inhibit infection of Uukuniemi virus (a bunyavirus) suggesting common requirements among late penetrating enveloped viruses. The results established class I HDACs as powerful regulators of microtubule organization, centrosome function, endosome maturation, and infection by IAV and other late penetrating viruses.