Intravoxel incoherent motion (IVIM) is a diffusion-weighted magnetic resonance imaging (MRI) method that may be applied to the placenta to help diagnose abnormal pregnancies. IVIM requires prolonged scan times, followed by a model-based estimation procedure. Maternal or fetal motion during the scan affects the accuracy of this estimation. In this work, we proposed to address this challenging motion correction and data fitting problem by using additional anatomical information that is routinely collected at the beginning of the examination. Super-resolution reconstruction (SRR) was applied to these anatomical data, to provide a patient-specific, 3D isotropic, anatomic reference. Our first contribution is a novel framework with a two-step motion correction that uses both IVIM and the SRR anatomic data, accounting for both intra- and inter-scan, non-rigid motion. Our second contribution is an automation and acceleration of the IVIM data fitting, using a state-of-the-art Bayesian-type algorithm, modified with a preconditioned Crank-Nicholson (pCN) sampling strategy. The accuracy of the IVIM parameter fitting was improved by the proposed motion correction strategy, as assessed by the mean absolute fitting error in the region of interest, which was 4.14 before and 3.02 after correction (arbitrary units of signal intensity). The novel sampling strategy accelerated parameter estimation by 39% in average, with the same accuracy as that of the conventional Bayesian approach. In conclusion, the proposed method may be applied to obtain fast and reliable IVIM parameter estimates in challenging scenarios such as prenatal MRI.