Intraplate tectonism has produced large-scale folding that steers regional drainage systems, such as the 1600 km-long Cooper Ck, en route to Australia's continental depocentre at Lake Eyre. We apply cosmogenic 10Be exposure dating in bedrock, and luminescence dating in sediment, to quantify the erosional and depositional response of Cooper Ck where it incises the rising Innamincka Dome. The detachment of bedrock joint-blocks during extreme floods governs the minimum rate of incision (17.4±6.5 mm/ky) estimated using a numerical model of episodic erosion calibrated with our 10Be measurements. The last big-flood phase occurred no earlier than ∼112–121 ka. Upstream of the Innamincka Dome long-term rates of alluvial deposition, partly reflecting synclinal-basin subsidence, are estimated from 47 luminescence dates in sediments accumulated since ∼270 ka. Sequestration of sediment in subsiding basins such as these may account for the lack of Quaternary accumulation in Lake Eyre, and moreover suggests that notions of a single primary depocentre at base-level may poorly represent lowland, arid-zone rivers. Over the period ∼75–55 ka Cooper Ck changed from a bedload-dominant, laterally-active meandering river to a muddy anabranching channel network up to 60 km wide. We propose that this shift in river pattern was a product of base-level rise linked with the slowly deforming syncline–anticline structure, coupled with a climate-forced reduction in discharge. The uniform valley slope along this subsiding alluvial and rising bedrock system represents an adjustment between the relative rates of deformation and the ability of greatly enhanced flows at times during the Quaternary to incise the rising anticline. Hence, tectonic and climate controls are balanced in the long term.