We evaluate the no-boundary path integral exactly in a Bianchi type IX minisuperspace with two scale factors. In this model the no-boundary proposal can be implemented by requiring one scale factor to be zero initially together with a judiciously chosen regularity condition on the momentum conjugate to the second scale factor. Taking into account the nonlinear backreaction of the perturbations we recover the predictions of the original semiclassical no-boundary proposal. In particular we find that large perturbations are strongly damped, consistent with vacuum state wave functions.