Draining from a closed-top tube occurs by downward displacement of liquid by air. The air volume grows inside the tube as an axisymmetric bullet-shaped finger similar to the Taylor bubble observed in gas–liquid slug flows, and the liquid drains as an annular film between the finger and the tube wall. The present study investigates the draining of shear-thinning vis-à-vis Newtonian liquids from closed-top circular millichannels. Numerical simulations using the phase-field method suggest that both the power law and Carreau models give close predictions of draining behavior in the investigated domain, i.e., for shear rate >0.1 s−1. The results are validated against experimental measurements based on high-speed photography and particle image velocimetry during the draining of aqueous solutions of carboxymethyl cellulose, xanthan gum, and glycerol. Further validations are performed for shear-thinning (using the power law, Carreau, and Carreau–Yasuda models) and Newtonian liquids with literature data on Taylor bubble rise in stationary liquid columns. The simulations using the power law model are used to explore additional insights into the flow physics. An increase in the apparent viscosity of shear-thinning liquids (by increasing the flow behavior index and/or flow consistency index) slows down the rate of Taylor finger growth. Increased liquid viscosity also results in a slender Taylor finger and leaves a higher amount of undrained liquid at the end of film-wise draining. The draining rate is a more significant function of flow behavior index n of the power law model for highly shear-thinning liquids (n < 0.6).