Fold and thrust belt architecture may be influenced by basement geometry of the downgoing plate. This influence is notoriously difficult to assess due to a common lack of subsurface constraints and low resolution of exhumation estimates in space and time. The Bohemian Spur is a basement high at the transition from the Alps to the Carpathians. It coincides with narrowing of the foreland basin and an orogen-scale change of strike. Its location in one of the best-studied orogens in the world makes it an ideal case for understanding how basement topography influences fold and thrust belt tectonics. However, since thermochronological studies were mainly focused on the core of the Alps, timing and amount of exhumation remain poorly constrained in these peripheral parts of the orogen. We present new apatite (U-Th)/He and fission track data from the wedge above the Bohemian Spur. Thermally reset ages monitor a so far un(der)appreciated phase of prominent Late Oligocene to Miocene cooling, associated with crustal thickening, uplift and erosion during wedge propagation. Pronounced exhumation on the order of 3–4.5 km can be related to basement steps beneath the advancing wedge. The spur acted as a buttress for foreland-propagating thrusting, pinning deformation and nucleating antiformal stacking and duplexing and thus exhumation above it. We illustrate how along- and across-strike changes of sub-detachment topography impact wedge propagation and control fold and thrust belt geometries. The buttressing effect accounts for most of the exhumation, while deep-seated slab dynamics are of subordinate importance for wedge uplift.