The centers of the core-collapse supernovae are one of the densest environments in the Universe. Under such conditions, it is conceivable that a first-order phase transition from ordinary nuclear matter to the quark-gluon plasma occurs. This transition releases a large amount of latent heat that can drive a supernova explosion and may imprint a sharp signature in the neutrino signal. We show how this snap feature, if observed at large-scale neutrino detectors, can set competitive limits on the neutrino masses and assist the localization of the supernova via triangulation. The 95% C.L. limit on the neutrino mass can reach 0.16 eV in Ice-Cube, 0.22 eV in Hyper-Kamiokande, and 0.58 eV in DUNE, for a supernova at a distance of 10 kpc. For the same distance and in the most optimistic neutrino conversion case, the triangulation method can constrain the 1 sigma angular uncertainty of the supernova localization within similar to 0.3 degrees-9.0 degrees in the considered pairs of the detectors, leading to an improvement up to an order of magnitude with respect to the often considered in the literature rise time of the neutronization burst.