Apoptosis is a highly regulated process crucial for maintaining cellular homeostasis and development. The B-cell lymphoma 2 (Bcl-2) family of proteins play a crucial role in regulating apoptosis. Overexpressed Bcl-2 proteins are associated with the development and progression of several human cancers. Annona muricata is a tropical plant that belongs to the Annonaceae family and is well known for its anticancer properties. In this study, molecular docking and simulations were performed to investigate the inhibitory potential of phytochemicals present in A. muricata against antiapoptotic proteins of the Bcl-2 family including Bcl-2, B-cell lymphoma extra-large (Bcl-Xl), and Mcl-1. Docking results revealed that the acetogenins, such as annomuricin A, annohexocin, muricatocin A, annomuricin-D-one, and muricatetrocin A/B, exhibited strong binding interactions with Bcl-Xl when compared to Bcl-2 and Mcl-1. Binding score and interactions of these acetogenins were notably better than those of currently available synthetic and natural inhibitors. Molecular dynamics simulations of the top-scoring lead molecules established that these molecules could bind strongly and consistently in the active site of Bcl-Xl. These results suggest that acetogenins could be explored as selective natural inhibitors of Bcl-Xl that could assist in promoting the intrinsic pathway of apoptosis.