Broad disagreement persists between helioseismological observables and predictions of solar models computed with the latest surface abundances. Here we show that most of these problems can be solved by the presence of asymmetric dark matter coupling to nucleons as the square of the momentum q exchanged in the collision. We compute neutrino fluxes, small frequency separations, surface helium abundances, sound speed profiles, and convective zone depths for a number of models, showing more than a 6σ preference for q^{2} models over others, and over the standard solar model. The preferred mass (3 GeV) and reference dark matter-nucleon cross section (10^{-37} cm^{2} at q_{0}=40 MeV) are within the region of parameter space allowed by both direct detection and collider searches.