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We report the first incision rates derived from burial ages of cave sediments from the Mur river catchment at the eastern margin of the Eastern Alps. At the transition zone between the Alpine orogen and the Pannonian basin, this river passes through the Paleozoic of Graz — a region of karstifiable rocks called the Central Styrian Karst. This river dissects the study area in a north–south direction and has left behind an abundance of caves. These caves can be grouped into several distinct levels according to their elevation above the present fluvial base level. Age estimates of abandoned cave levels are constrained by dating fluvial sediments washed into caves during the waning stages of speleogenesis with the terrestrial cosmogenic nuclide method. These ages and the elevations of the cave levels relative to the current valley floor are used to infer a very complex history of 4 million years of water table position, influenced by the entrenchment and aggradation of the Mur river. We observe rather low rates of bedrock incision over the last 4 Ma (in the order of 0.1 mm/y) with an e-folding decrease in this trend to lower rates at younger times. We relate this incision history to a tectonic setting where an increase of drainage area of the Mur river due to stream piracy in Late Miocene to Pliocene times is linked to surface uplift. The later decrease in valley lowering rates is attributed to the rise of the base level related to aggradation of sediments within the valley. Sediment transport through the valley from the upstream section of the Mur river limited the erosional potential of the river to a transport limited state at the later stages of the incision history.