We present spatially resolved far-ultraviolet spectra (912-1840 Angstrom) of NGC 1068 obtained using the Hopkins Ultraviolet Telescope (HUT) during the 1995 March Astro-2 mission. Three spectra of this prototypical Seyfert 2 galaxy were obtained through a 12 " diameter aperture centered on different locations near the nucleus. The first pointing (A1) was centered west of the optical nucleus; the nucleus was on the eastern edge of the aperture. The second (A2) was centered southwest of the optical nucleus with the nucleus well inside the aperture. The third (B) was centered on the ionization cone, with the nucleus on the southwestern edge of the aperture. While all three aperture locations have spectra similar to the Astro-1 observations of Kriss et al., these new spatially resolved observations localize the source of the far-UV line and continuum emission. The ionization cone (location B) has both brighter emission lines and continuum than the nuclear region (location A2). Position A1 is fainter than either A2 or B in both lines and continuum. The far-UV emission lines observed with HUT have a spatial distribution that most closely resembles that of [O III] lambda 5007 but appear to be more extended and offset to the northeast along the axis of the radio jet. This supports the previous conclusion of Kriss et al, that the bright C III lambda 977 and N III lambda 991 arises in shock-heated gas. The UV continuum radiation has a more extended spatial distribution than the line-emitting gas. At wavelengths longward of 1200 Angstrom, the inferred continuum distribution is consistent with that seen in archival Hubble Space Telescope WFPC2 images through filter F218W and it appears to contain a substantial contribution from starlight. At wavelengths shorter than 1200 Angstrom the UV continuum becomes more concentrated in a region matching the location and shape of the UV line radiation, consistent with nuclear flux scattered by a combination of the electron scattering mirror and the northeast dust cloud.