The intermediate polar EX Hya was observed in 1995 March with the Hopkins Ultraviolet Telescope on the Astro-2 space shuttle mission. The time-resolved, 820-1860 Angstrom data that were obtained are the first spectra of an intermediate polar to extend to the Lyman limit. They cover phases phi(67) = 0.05-0.50 of the 67 minute white dwarf rotational period. Fitted to a blackbody, the continuum has an effective temperature of about 25,000 K. At phi(67) = 0.0, the spectrum shows strong, broad (greater than or similar to 2500 km s(-1) FWHM) lines of C IV lambda 1549, C III lambda 977, lambda 1176, N V lambda 1240, Si IV lambda 1394, and a blend of lines including Ly beta and O VI lambda 1034. The line ratios suggest a photoionized emission region with densities greater than or similar to 10(13) cm(-3). As the phase increases to 0.5, the line fluxes drop by more than a factor of 4, but the continuum flux declines by only similar to 20%. There are +/- 30% fluctuations in the continuum flux, but not the lines, on timescales of less than a minute during the second half of the observation, which suggests that the lines and continuum arise in physically distinct regions of the accretion how. These data are compatible with models of EX Hya in which the UV lines arise mainly in an optically thick accretion curtain and the UV continuum arises in the innermost part of the accretion curtain and/or the heated face of the white dwarf. The profile of the C IV lambda 1549 line changes considerably over the course of the observation, with a strong absorption appearing on the blue wing of the line from phi(67) = 0.36 to the end of the observation.