We clarify the nature of the small-diameter supernova remnant (SNR) Kes 73 and its central compact source, 1E 1841-045, using X-ray data acquired with ASCA. We introduce a spatiospectral decomposition technique necessary to disentangle the ASCA spectrum of the compact source from the barely resolved shell-type remnant. The source spectrum (1-8 keV) is characterized by an absorbed power law with a photon index α 3.4 and N_H 3.0 × 10²² cm^-2, possibly nonthermal in nature. This bright X-ray source is likely a slowly spinning pulsar, whose detection is reported in our companion paper. The SNR spectrum is characteristic of a thermal plasma, with kT 0.6 keV and emission lines typical of a young remnant. The element Mg and possibly O and Ne are found to be overabundant, qualitatively suggesting an origin from a massive progenitor. We find that Kes 73 is a young (2000 yr) Type II/Ib SNR containing a neutron star pulsar spinning anomalously slowly for its age. Kes 73 is yet another member of a growing class of SNRs containing radio-quiet compact sources with a hard spectral signature.