Phage therapy remains a potential treatment for bacterial infections. Yet, the slow progress in realizing clinical therapeutics is matched by a similar dearth in principled understanding of how phage therapy works. Theoretical models and in vitro experiments find that combining phage and bacteria often leads to coexistence or phage elimination altogether. Both outcomes stand in contrast to the stated goals of phage therapy. Here, we propose a phage therapy model that considers the nonlinear dynamics arising from interactions between bacteria, phage, and the immune system. We analytically identify a synergistic regime in which phage and the immune response jointly contribute to the elimination of target bacteria. Crucially, we find that in this synergistic regime, neither phage alone nor the immune system alone can eliminate the bacteria. We utilize numerical simulations to explore the synergistic effect and its significance for guiding the use of phage therapy in clinically relevant applications.