We present a modular error mitigation protocol for running BQP computations on a quantum computer with time-dependent noise. Utilising existing tools from quantum verification and measurement-based quantum computation, our framework interleaves standard computation rounds alongside test rounds for error-detection and inherits an exponential bound (in the number of circuit runs) on the probability that a returned classical output is correct. We repurpose these ideas in an error mitigation context, introducing a post-selection technique called basketing to address time-dependent noise behaviours and reduce overhead. The result is a first-of-its-kind error mitigation protocol which is exponentially effective and requires minimal noise assumptions, making it straightforwardly implementable on existing, NISQ devices and scalable to future, larger ones. We demonstrate the protocol experimentally using classical noisy simulation, presenting a measurement pattern which directly maps to (and can be tiled on) the heavy-hex layout of current IBM hardware.