We study the direct calculation of total energy derivatives for lattice dynamics and electronphonon coupling calculations using supercell matrices with non-zero off-diagonal elements. We show that it is possible to determine the response of a periodic system to a perturbation characterized by a wave vector with reduced fractional coordinates (m₁/n₁, m₂/n₂, m₃/n₃) using a supercell containing a number of primitive cells equal to the least common multiple of n₁, n₂, and n₃. If only diagonal supercell matrices are used, a supercell containing n₁n₂n₃ primitive cells is required. We demonstrate that the use of non-diagonal supercells significantly reduces the computational cost of obtaining converged zero-point energies and phonon dispersions for diamond and graphite. We also perform electron-phonon coupling calculations using the direct method to sample the vibrational Brillouin zone with grids of unprecedented size, which enables us to investigate the convergence of the zero-point renormalization to the thermal and optical band gaps of diamond.