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The fusion of lipid membranes is opposed by high energetic barriers. In living organisms, complex protein machineries carry out this biologically essential process. Here we show that membrane-spanning carbon nanotubes (CNTs) can trigger spontaneous fusion of small lipid vesicles. In coarse-grained molecular dynamics simulations, we find that a CNT bridging between two vesicles locally perturbs their lipid structure. Their outer leaflets merge as the CNT pulls lipids out of the membranes, creating an hourglass-shaped fusion intermediate with still intact inner leaflets. As the CNT moves away from the symmetry axis connecting the vesicle centers, the inner leaflets merge, forming a pore that completes fusion. The distinct mechanism of CNT-mediated membrane fusion may be transferable, providing guidance in the development of fusion agents, e.g., for the targeted delivery of drugs or nucleic acids.