This manuscript contains the modeling and analysis of an unsteady Carreau fluid with a magnetohydrodynamical effect over a stretching sheet. The governing momentum and energy equations admit a self-similarity solution. The system of ordinary differential equations has been solved analytically by the homotopy analysis method (HAM) and numerically by BVP4C (Matlab routine). An analysis of results shows that obtained analytical and numerical solutions are in excellent agreement with existing results in the literature. Furthermore, the effect of various fluid parameters on the velocity and temperature profiles are studied graphically. It is observed that velocity increases in the stretching sheet for power law index n and the Weissenberg number We, whereas it decreases for magnetic parameter M2. Tabular analysis on skin friction and heat transfer rate is also presented against pertinent fluid parameters.