Functional magnetic resonance imaging (fMRI) is a powerful and broadly used means of non-invasively mapping human brain activity. However fMRI is an indirect measure that rests upon a mapping from neuronal activity to the blood oxygen level dependent (BOLD) signal via hemodynamic effects. The quality of estimated neuronal activity hinges on the validity of the hemodynamic model employed. Recent work has demonstrated that the hemodynamic response has non-separable spatiotemporal dynamics, a key property that is not implemented in existing fMRI analysis frameworks. Here both simulated and empirical data are used to demonstrate that using a physiologically based model of the spatiotemporal hemodynamic response function (stHRF) results in a quantitative improvement of the estimated neuronal response relative to unphysical space-time separable forms. To achieve this, an integrated spatial and temporal deconvolution is established using a recently developed stHRF. Simulated data allows the variation of key parameters such as noise and the spatial complexity of the neuronal drive, while knowing the neuronal input. The results demonstrate that the use of a spatiotemporally integrated HRF can avoid "ghost" neuronal responses that can otherwise be falsely inferred. Applying the spatiotemporal deconvolution to high resolution fMRI data allows the recovery of neuronal responses that are consistent with independent electrophysiological measures.