Biological transmission of vesicular content occurs by opening of a fusion pore. Recent experimental observations have illustrated that fusion pores between vesicles that are docked by an extended flat contact zone are located at the edge (vertex) of this zone. We modeled this experimentally observed scenario by coarse-grained molecular simulations and elastic theory. This revealed that fusion pores experience a direct attraction toward the vertex. The size adopted by the resulting vertex pore strongly depends on the apparent contact angle between the adhered vesicles even in the absence of membrane surface tension. Larger contact angles substantially increase the equilibrium size of the vertex pore. Because the cellular membrane fusion machinery actively docks membranes, it facilitates a collective expansion of the contact zone and increases the contact angle. In this way, the fusion machinery can drive expansion of the fusion pore by free energy equivalents of multiple tens of k _B T from a distance and not only through the fusion proteins that reside within the fusion pore.