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The process of one fluid pushing another is universally common while involving complex interfacial instabilities. Particularly, occurring in a myriad of natural and industrial processes, wavy fingering patterns frequently emerge when a less viscous fluid pushes another more viscous one, such as water invading oil, in a porous medium. Such finger-shaped interfaces producing partial displacement significantly affect the efficiency of numerous applications, for example, chromatography, printing devices, coating flows, oil-well cementing, as well as large-scale technologies of groundwater and enhanced oil recovery (EOR). This classical viscous fingering instability is notoriously difficult to control because the two fluids' viscosity or mobility ratio is often fixed and yet the predominant drive of the instability. Although some strategies have been recently revealed for simple fluids of constant viscosity, the feasibility of controlling the fundamental viscous fingering instability for omnipresent complex fluids has not been established. Here, we demonstrate how to control a common complex fluid (of a power-law fluid with a yield-stress) using a narrow tapered cell theoretically and experimentally.