Within the series of ternary rare-earth transition metal carbides Sc₃TC₄ (T = Fe, Co, Ni) only the Co congener displays a structural phase transition at 72 K and an onset of bulk superconductivity at 4.5 K. In this paper we present the results of a detailed analysis of the structural, electronic, and vibrational properties of the low-temperature phase of Sc₃CoC₄ that represents one of the few well-documented examples of a quasi one-dimensional (1D) superconductor. Variable temperature neutron powder diffraction and low temperature X-ray diffraction experiments were performed in order to confirm the subtle structural distortions during the phase transition. The results of periodic electronic structure calculations indicate, that the structural transition can clearly be identified as a Peierls-type distortion and by a comparison with the isostructural carbide Sc₃FeC₄ we are able to identify the chemical, electronic, and the vibrational control parameters of the transition. Topological analyses of the electron density distribution and of the valence shell charge concentrations at the cobalt atom finally allow us to directly correlate the changes in the electronic structure due to the Peierls transition in reciprocal space with the according subtle changes in the real space properties of Sc₃CoC₄.