In the manufacturing sector, transport phenomena near the stagnation region are frequent, particularly in the polymer and extrusion processes, which require continuous improvement to raise the process’s quality standards. The aim of this study is to explore the improvement of heat and mass transmission using unsteady magnetohydrodynamic (MHD) hybrid nanofluid (HNF) flow over a stretching/shrinking cylinder with variable viscosity and Stefan blowing. The governed equations of heat and mass transfer processes are converted into ordinary differential equations (ODEs) using the appropriate transformations, and the resulting equations are then solved using the MATLAB package bvp4c. With an upsurge in the volume fraction of nanoparticles, the skin friction increases, but the reverse trend is detected with negative values for the unsteadiness constraint. The use of 2D graphs to show how important parameters affect the velocity, temperature, and concentration is thoroughly discussed. There is a discussion of the quantitative findings from the wall shear factor and the heat and mass transfer rates calculated for the stretching/shrinking cases.