We have detected EUV emission from the globular cluster NGC 1851, using the Deep Survey Photometer aboard the Extreme Ultraviolet Explorer (EUVE). The minimum EUV luminosity implied by our detection is similar to 10(35) - 10(36) ergs s(-1), for a distance and reddening appropriate to NGC 1851. This is only the second detection of a globular cluster at EW energies. If this flux is due to the cluster LMXB X0512-401, then the observed EUV luminosity is likely to be comparable to the 2-10 keV X-ray luminosity of the LMXB. With the detection of EUV emission from M15, these observations suggest that the EUV flux of LMXBs in general may represent a sizable fraction of their total bolometric luminosity. However, additional observations are needed to conclusively show that these cluster LMXBs (X0512-401 and AC211) indeed dominate the cluster EUV emission. Finally, we compare our NGC 1851 measurement with the EUVE detection of the X-ray transient XTE J1118+480 during outburst, and show that these objects appear to have comparable EW luminosities.