Expression of E7 proteins encoded by carcinogenic, high-risk human papillomaviruses (HPVs) triggers increased expression of the histone H3 lysine 27 demethylase KDM6A. KDM6A expression is necessary for survival of high-risk HPV E7 expressing cells, including several cervical cancer lines. Here we show that increased KDM6A in response to high-risk HPV E7 expression causes epigenetic de-repression of the cell cycle and DNA replication inhibitor p21CIP1, and p21CIP1 expression is necessary for survival of high-risk HPV E7 expressing cells. The requirement for KDM6A and p21CIP1 expression for survival of high-risk HPV E7 expressing cells is based on p21CIP1's ability to inhibit DNA replication through PCNA binding. We show that ectopic expression of cellular replication factors can rescue the loss of cell viability in response to p21CIP1 and KDM6A depletion. Moreover, we discovered that nucleoside supplementation will override the loss of cell viability in response to p21CIP1 depletion, suggesting that p21CIP1 depletion causes lethal replication stress. This model is further supported by increased double strand DNA breaks upon KDM6A or p21CIP1 depletion and DNA combing experiments that show aberrant re-replication upon KDM6A or p21CIP1 depletion in high-risk HPV E7 expressing cells. Therefore, KDM6A and p21CIP1 expression are essential to curb E7 induced replication stress to levels that do not markedly interfere with cell viability.