Depression is a serious psychiatric disorder that affects millions of individuals all over the world, thus demanding special attention from researchers in order to investigate its effective remedies. Curcumin, along with its synthetic derivatives, is recognized for its incredible pharmacological activities. In this study, methyl, methoxy and chloro-substituent synthetic curcumin analogues C1–C3 were respectively tested for free radical-scavenging activity. Behavioral studies were performed using chemical-induced and swimming endurance tests as stress models, and forced swim tests (FSTs) and tail suspension tests (TSTs) as depression mice models. Biochemical examinations were performed after a scopolamine-induced stress model by decapitating the mice, and brain tissues were isolated for biochemical assessment of catalase (CAT), superoxide dismutase (SOD), glutathione (GSH), and malondialdehyde (MDA). The curcumin analogue C2 exhibited higher DPPH (2,2-diphenyl-1-picrylhydrazyl) and ABTS (2,2′-azinobis-3-ethylbenzothiazo-line-6-sulphonate) free radical-scavenging potential, having IC50 values of 45.18 µg/mL and 62.31 µg/mL, respectively, in comparison with reference curcumin and tocopherol. In the chemical-induced test, C2 (80.17%), C3 (72.79%) and C1 (51.85%) revealed higher antistress responses by significantly reducing the number of writhes, whereas the immobility time was significantly reduced by C2 and C3 in the swimming endurance test, indicating excellent antistress potential. Similarly, C2 and C3 significantly reduced the immobility times in FST and TST, demonstrating their antidepressant properties. The biomarkers study revealed that these compounds significantly enhanced hippocampus CAT, SOD and GSH, and reduced MDA levels in the scopolamine-induced stress mice model. These findings suggest the potential of curcumin analogues (C2 and C3) as antistress and antidepressant agents.