Despite non-Newtonian fluids being involved in many industrial processes, e.g., in food and chemical industries, their thermal treatment still represents a significant challenge due to their generally high apparent viscosity and consequent low heat transfer capability. Heat transfer in heat exchangers can be enhanced by passive systems, such as inserts or fins, to promote boundary layer disruption and fluid recirculation. However, most of the existing configurations cannot significantly improve the heat transfer over pressure drops in deep laminar flows. The present paper presents a numerical investigation on non-Newtonian flows passing through the annulus side of a double-pipe heat exchanger with staggered helical fins. The adopted geometry was conceptualized by merging the beneficial effects of swirling flow devices and boundary layer disruption. The numerical results were first validated against analytical solutions for non-Newtonian flows in annuli under a laminar flow regime. The finned geometry was therefore numerically tested and compared with the bare annulus to quantify the resulting heat transfer augmentation. When compared with the bare annuli, the proposed novel geometry greatly enhanced the heat transfer while mitigating friction losses.