Characterizing the complex interplay of cellular processes in cancer would enable the discovery of key mechanisms underlying its development and progression. Published approaches to decipher driver mechanisms do not explicitly model tissue-specific changes in pathway networks and the regulatory disruptions related to genomic aberrations in cancers. We therefore developed InFlo, a novel systems biology approach for characterizing complex biological processes using a unique multidimensional framework integrating transcriptomic, genomic and/or epigenomic profiles for any given cancer sample. We show that InFlo robustly characterizes tissue-specific differences in activities of signalling networks on a genome scale using unique probabilistic models of molecular interactions on a per-sample basis. Using large-scale multi-omics cancer datasets, we show that InFlo exhibits higher sensitivity and specificity in detecting pathway networks associated with specific disease states when compared to published pathway network modelling approaches. Furthermore, InFlo's ability to infer the activity of unmeasured signalling network components was also validated using orthogonal gene expression signatures. We then evaluated multi-omics profiles of primary high-grade serous ovarian cancer tumours (N=357) to delineate mechanisms underlying resistance to frontline platinum-based chemotherapy. InFlo was the only algorithm to identify hyperactivation of the cAMP-CREB1 axis as a key mechanism associated with resistance to platinum-based therapy, a finding that we subsequently experimentally validated. We confirmed that inhibition of CREB1 phosphorylation potently sensitized resistant cells to platinum therapy and was effective in killing ovarian cancer stem cells that contribute to both platinum-resistance and tumour recurrence. Thus, we propose InFlo to be a scalable and widely applicable and robust integrative network modelling framework for the discovery of evidence-based biomarkers and therapeutic targets.