Cellular mechanisms that safeguard genome integrity are often subverted in cancer. To identify cancer-related genome caretakers, we employed a convergent multi-screening strategy coupled to quantitative image-based cytometry and ranked candidate genes according to multivariate readouts reflecting viability, proliferative capacity, replisome integrity, and DNA damage signaling. This unveiled regulators of replication stress resilience, including components of the pre-mRNA cleavage and polyadenylation complex. We show that deregulation of pre-mRNA cleavage impairs replication fork speed and leads to excessive origin activity, rendering cells highly dependent on ATR function. While excessive formation of RNA:DNA hybrids under these conditions was tightly associated with replication-stress-induced DNA damage, inhibition of transcription rescued fork speed, origin activation, and alleviated replication catastrophe. Uncoupling of pre-mRNA cleavage from co-transcriptional processing and export also protected cells from replication-stress-associated DNA damage, suggesting that pre-mRNA cleavage provides a mechanism to efficiently release nascent transcripts and thereby prevent gene gating-associated genomic instability. Replication stress is a hallmark of many cancers. Teloni et al. identify the pre-mRNA cleavage factor WDR33 as regulator of replication stress resilience and demonstrate that, when WDR33 function is impaired, unreleased nascent transcripts and genomic loci re-localize toward the nuclear periphery, where they cause replication stress and DNA damage.