In this paper, a mathematical foundation has been developed for the primary understanding of complex interaction of the wall slip with the Coriolis and Lorentz forces acting orthogonally on the Electromagnetohydrodynamic (EMHD) flow of a power-law fluid in a microchannel. Modified Navier Stokes equations are solved numerically by incorporating the fully implicit computational scheme with suitable initial and boundary conditions, which generates numerical results in excellent comparison with the literature for a certain limiting case. An extensive effort has been made to understand how the Hartmann number, fluid behavior index, rotating Reynolds number, and slip parameter affects the flow. Results show the velocity of the power-law fluid depends strongly on flow parameters. Critical Hartmann number can be obtained for the power-law fluid in presence of uniform electric and magnetic fields. As a promising phenomenon, existence of a cross over point (which depends upon the fluid behavior index) for the centerline flow velocity, has also been predicted. Reduction in the shear stress and fluid viscosity can be controlled effectively by incorporating a slippery film of lubricant on the periphery of the microchannel. This work is useful to meet the upcoming challenges of future generation, like improvement in bio-magnetic-sensor technologies as well as electrical and mechanical mechanisms.