Carbon capture and storage (CCS) is commonly acknowledged as a valuable technology for reducing industrial emissions. However, limited installation capacity raises questions about its ability to scale up effectively and promptly. This issue can, in part, be attributed to expensive and energy-intensive processes, as well as the poorly-understood role of heat- and material integration. Here, we show that net-zero and net-negative industrial sectors are possible by integrating capture and mineralization in cement production, steel manufacture, and waste incineration. These sectors feature large amounts of waste heat, alkaline solid residues, and process emissions. We estimate that the three sectors combined could reduce European emissions by 27% (c.a. 860 Mton), with marginal abatement costs between 62 and 85 EUR per ton of CO2. These values compare favorably with deploying capture and storage separately, with economic benefits of up to 50%. Moreover, CCS needs to be considered within an industrial cluster to justify its economic and environmental deployment, with system integration being crucial when taking investment decisions.