  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 $\sim 0.3^{\circ}-9.0^{\circ}$ 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.
