A novel mechanism of boosting dark matter by cosmic neutrinos is proposed. The new mechanism is so significant that the arriving flux of dark matter in the mass window $1~{rm keV} lesssim m_{rm DM} lesssim 1~{rm MeV}$ on Earth can be enhanced by two to four orders of magnitude compared to one only by cosmic electrons. Thereby we firstly derive conservative but still stringent bounds and future sensitivity limits for such cosmic-neutrino-boosted dark matter ($ u$BDM) from advanced underground experiments such as Borexino, PandaX, XENON1T, and JUNO.