The alternating cycle of valley widening through lateral erosion ("strath planation") and valley narrowing through vertical incision into bedrock ("strath terrace abandonment") due to variations in sediment supply (Qs) relative to river transport capacity (Qsc) is a common feature in many mountainous environments, yet our understanding of the mechanics of the processes that drive this landscape change remains poorly quantified. Here, we use an experimental and numerical study to identify the geomorphic and hydraulic controls driving the response of mixed bedrock-alluvial rivers to variable sediment supply, water discharge, and tectonic tilting. The experimental channels exhibit a multistage response of channel narrowing, accompanied by stripping of the alluvial cover in a downstream-migrating incision wave, followed by destabilization of the bed and development of a single vertical step in the bed profile ("knickpoint") when the hydraulic conditions are supercritical. In our experiments, headward erosion by knickpoints is the most efficient process of strath terrace abandonment, contributing the majority of the total vertical incision in a short period of time. We show experimentally that knickpoint development under supercritical flow conditions drives the rapid response of fluvial systems to upstream perturbations in Qs/Qsc despite no base-level fall. This has implications for the understanding of distributions of strath terrace ages, the inference of base-level variations from knickpoint propagation, and how landscapes respond to climatic or tectonic perturbations.