Neutron-induced nuclear reactions play an important role in the Big Bang Nucleosynthesis. Their excitation functions are, from an experimental point of view, usually difficult to measure. Nevertheless, in the last decades, big efforts have led to a better understanding of their role in the primordial nucleosynthesis network. In this work, we apply the Trojan Horse Method to extract the cross section at astrophysical energies for the 3 He (n, p) 3 H reaction after a detailed study of the 2 H (3 He, pt) H three-body process. Data extracted from the present measurement are compared with other published sets. The reaction rate is also calculated, and the impact on the Big Bang nucleosynthesis is examined in detail.