A novel analysis is performed, incorporating time-of-flight (TOF) information to study the interactions of dark matter (DM) with standard model particles. After supernova (SN) explosions, DM with mass m_{χ}≲O(MeV) in the halo can be boosted by SN neutrinos (SNν) to relativistic speed. The SNν boosted DM (BDM) arrives on Earth with TOF which depends only on m_{χ} and is independent of the cross section. These BDMs can interact with detector targets in low-background experiments and manifest as afterglow events after the arrival of SNν. The characteristic TOF spectra of the BDM events can lead to large background suppression and unique determination of m_{χ}. New cross section constraints on sqrt[σ_{χe}σ_{χν}] are derived from SN1987a in the Large Magellanic Cloud with data from the Kamiokande and Super-Kamiokande experiments. Potential sensitivities for the next galactic SN with Hyper-Kamiokande are projected. This analysis extends the existing bounds on sqrt[σ_{χe}σ_{χν}] over a broad range of r_{χ}=σ_{χν}/σ_{χe}. In particular, the improvement is by 1-3 orders of magnitude for m_{χ}<O(100 keV) for σ_{χe}∼σ_{χν}. Prospects of exploiting TOF information in other astrophysical systems to probe exotic physics with other DM candidates are discussed.