The branching ratios and supercollider cross sections of the two CP-even Higgs scalars h0 and H-0 of the minimal supersymmetric model (MSSM) are computed (including the effects of leading log radiative corrections). The "gold-plated" Higgs-boson decay into ZZ --> l+l-l+l- is analyzed at the CERN Large Hadron Collider and Superconducting Super Collider, and the regions of MSSM Higgs sector parameter space where the h0 or H-0 can be detected in this mode are delineated. The prospects for Higgs-boson detection as a function of the detector resolution are discussed. The viability of other decay modes for detecting the h0 and H-0 is briefly considered.