We report the possibility of achieving an order of magnitude reduction in the energy dissipation needed to write bits in perpendicular magnetic tunnel junctions by simulating the magnetization dynamics under a combination of resonant surface acoustic waves (r-SAWs) and spin-transfer-torque (STT). The magnetization dynamics were simulated using the Landau-Lifshitz-Gilbert equation under macrospin assumption with the inclusion of thermal noise. The resonant magnetization dynamics in the magnetostrictive nanomagnet builds over few tens of cycles of SAW application that drives the magnetization to precess in a cone with a deflection of ∼45° from the perpendicular direction. This reduces the STT current density required to switch the magnetization direction without increasing the STT application time or degrading the switching probability in the presence of room temperature thermal noise. This could lead to a pathway to achieve energy efficient switching of spin-transfer-torque random access memory whose lateral dimensions can be scaled aggressively despite using materials with low magnetostriction by employing SAW excitation to drive ferromagnetic resonance.