Many enveloped viruses infect cells via fusion to endosomes, but controlling this process within living cells has been challenging. We studied the fusion of influenza virus virions to endosomes in a chemically controllable manner. Extracting virus:endosome conjugates from cells and exogenously triggering fusion permits precise study of virus:endosome fusion kinetics. Surprisingly, endosomal curvature does not grossly alter fusion kinetics, although membrane deformability does. This supports a model for influenza virus entry where cells restrict or permit membrane fusion by changing deformability, for instance, using interferon-induced proteins.