Abstract: Recently, the BESIII Collaboration observed the three-body decays D-s(+) -> eta omega pi(+), D+ -> Kappa(0)(S)pi(+)omega, and D-0 -> Kappa pi(+)omega. In this study, we investigate the contributions of the subprocesses rho(+) -> omega pi(+) in these Cabibbo-favored decays D -> h omega pi, with rho(+) = {rho(770)(+),rho(1450)(+),rho(770)(+)&rho(1450)(+)} and h = {eta, Kappa(0)(S), K- }, by introducing these subprocesses into the decay amplitudes of the relevant decay processes via the vector form factor F-omega pi, which has been measured in the related rand e(+)e(-) processes. We provide the first theoretical predictions for the branching fractions of the quasi-two-body decays D-s(+) -> eta[rho(+) -> ] omega pi(+), D+ -> Kappa(0)(S) [rho* ->]omega pi(+), and D-0 -> Kappa(-)[rho(+) ->]omega pi(+). Our findings reveal that the contributions from the subprocess rho(770)(+) omega pi(+) are significant in these observed three-body decays D-s(+) -> eta omega pi(+), D+ -> Kappa(0)(S)omega pi(+), and D-0 -> Kappa(-)omega pi(+), notwithstanding the contributions originating from the Breit-Wigner tail effect of rho(770)(+). The numerical results of this study suggest that the dominant resonance contributions for the three-body decays D-s(+) -> eta omega pi(+) and D+ -> Kappa(0)(S)omega pi(+) originate from the P-wave intermediate states rho(770), rho(1450) and their interference effects.