BK polyomavirus (BKPyV) is a small DNA virus that establishes a life-long persistent infection in the urinary tract of most people. BKPyV is known to cause severe morbidity in renal transplant recipients and can lead to graft rejection. The simple 5.2 kilobase pair dsDNA genome expresses just seven known proteins, thus it relies heavily on host machinery to replicate. How the host proteome changes over the course of infection is key to understanding this host:virus interplay. Here for the first time quantitative temporal viromics has been used to quantify global changes in >9,000 host proteins in two types of primary human epithelial cell throughout 72 hours of BKPyV infection. These data demonstrate the importance both of cell cycle progression and pseudo-G2 arrest in effective BKPyV replication, along with a surprising lack of innate immune response throughout the whole virus replication cycle. BKPyV thus evades pathogen recognition to prevent activation of innate immune responses in a sophisticated manner.