Magnetic resonance imaging (MRI) has become an unrivalled medical diagnostic technique able to map tissue anatomy and physiology non-invasively. MRI measurements are meticulously engineered to control experimental conditions across the sample. However, residual radiofrequency (RF) field inhomogeneities are often unavoidable, leading to artefacts that degrade the diagnostic and scientific value of the images. Here we show that, paradoxically, these artefacts can be eliminated by deliberately interweaving freely varying heterogeneous RF fields into a magnetic resonance fingerprinting data-acquisition process. Observations made based on simulations are experimentally confirmed at 7 Tesla (T), and the clinical implications of this new paradigm are illustrated with in vivo measurements near an orthopaedic implant at 3T. These results show that it is possible to perform quantitative multiparametric imaging with heterogeneous RF fields, and to liberate MRI from the traditional struggle for control over the RF field uniformity.