The Rungwe Volcanic Province (RVP) is a volcanic center in an anomalous region of magma-assisted rifting positioned within the magma-poor Western Branch of the East African Rift (EAR). The source of asthenospheric melt for the RVP is enigmatic, particularly since the volcanism is highly localized, unlike the Eastern Branch of the EAR. Some studies suggest the source of asthenospheric melt beneath the RVP arises from thermal perturbations in the upper mantle associated with an offshoot of the African Superplume flowing from the SW, while others propose a similar mechanism, but from the Kenyan plume diverted around the Tanzania Craton from the NE. Another possibility is decompression melting from upwelling asthenosphere due to lithospheric modulated convection (LMC) where the lithosphere is thin. We test the hypothesis that asthenospheric melt feeding the RVP can be generated from LMC. We develop a 3D thermomechanical model of LMC beneath the RVP and the entire Malawi Rift that incorporates melt generation. We assume a rigid lithosphere with laterally varying thickness and use non-Newtonian, temperature-, pressure- and porosity-dependent creep laws of anhydrous peridotite for the sublithospheric convecting mantle. We find decompression melt associated with LMC upwelling (~3 cm/yr) occurs at a maximum depth of ~150 km localized beneath the RVP. We also suggest asthenospheric upwelling due to LMC entrains plume materials that do not penetrate the transition zone into the melt. Decompression melting associated with upwelling due to LMC may also provide melt sources for other continental regions of thinned lithosphere.