Gastroesophageal adenocarcinoma (GEA) is an aggressive, often lethal, malignancy that displays marked chromosomal instability (CIN). To understand adaptive responses that enable CIN, we analyzed paired normal, premalignant, and malignant gastric lesions from human specimens and a carcinogen-induced mouse model, observing activation of replication stress, DNA damage response (DDR), and cell cycle regulator p21 in neoplastic progression. In GEA cell lines, expression of DDR markers correlated with ploidy abnormalities, including high-level focal amplifications and whole-genome duplication (WGD). Moreover, high expression of DNA damage marker H2AX correlated with CIN, WGD, and inferior patient survival. By developing and implementing a composite diagnostic score that incorporates TP53 mutation status, ploidy abnormalities, and H2AX expression, among other genomic information, we can identify GEA cell lines with enhanced sensitivity to DDR pathway inhibitors targeting Chk1/2 and Wee1. Anti-tumor properties were further augmented in combination with irinotecan (SN38) but not gemcitabine chemotherapy. These results implicate specific DDR biomarkers and ploidy abnormalities as diagnostic proxy that may predict premalignant progression and response to DDR pathway inhibitors.