Intraguild predation (IGP) is a type of interaction in which a top predator simultaneously competes and predates an intermediate prey that shares a third prey species with the top predator. While common in nature, most theoretical population dynamics models proposed in the literature predict that this three species interaction usually leads to extinction of the intermediate prey population. Predator-induced defenses are widely seen in these systems and should be incorporated in IGP models to promote coexistence. With this aim, we introduce a nonlinear response to the predation of IG-predator on IG-prey. The phase diagram of species coexistence is obtained as function of the attack efficiency and the degree of nonlinearity of the defense mechanism. Further we show how the nonlinearity affects the equilibrium populations. We unveil that there is an optimal nonlinearity at which the convergence towards the stationary coexistence regime is the fastest.