Tigernut (TN) is an underutilized crop with nutritional value that has remained untapped in producing extruded products. This research aims to establish the favorable extrusion conditions that produce a TN-based nutritive extruded snack with improved physicochemical characteristics. A collet extruder was used in this comparison study to examine the effects of formulation (60% TN flour and 40% brown rice [BR] vs. 60% TN flour and 40% Japonica rice [JR]). The effects of extrusion conditions, such as die temperature (90°C, 100°C, and 110°C) and screw speed (250, 300, and 350 rpm), on the physicochemical characteristics of extrudates were studied. TN-BR extrudates produced at 110°C and 350 rpm had the following improved characteristics: protein (6.09–7.33%), ash (1.40–1.59%), crude fat (7.15–9.90%), crude fiber (2.51–3.92%), reduced hardness (2.35–3.37 N), springiness (2.30–2.64), chewiness (234.71–256.72 N), bulk density (1.17–2.57 g/cm3), expansion ratio (1.65–2.24), color (L*: 68.86–74.30), water absorption index (2.69–3.45 g/g), water solubility index (13.95–21.75%), and oil absorption capacity (23.65–25.64 g/g). Extrudates produced at lower temperatures (90°C and 100°C) and screw speed (250 and 300 rpm) exhibited lesser surface consistency than the extrudates produced at 110°C and 350 rpm. The antioxidant activity and the total phenolic content (40.91–49.63 mg gallic acid equivalent/100 g) were improved significantly. Similar improvements were observed in TN-JR extrudates; however, TN-BR extrudates had better nutritional value (higher protein: 7.33%, higher ash: 1.59%, and higher antioxidant activity). The results could help with economic success, food nutrition improvement, and food security by exploiting the underutilized TN crop for sustainable extruded snacks production.