This paper proposes a robust and efficient oscillation-eliminating discontinuous Galerkin (OEDG) method for solving multicomponent chemically reacting flows, which is an extension and application of the recent work [M. Peng, Z. Sun, and K. Wu, Math. Comput., 2024, doi.org/10.1090/mcom/3998]. Following recently developed high-order bound-preserving discontinuous Galerkin method in [J. Du and Y. Yang, J. Comput. Phys., 469 (2022), 111548], we incorporate an OE procedure after each Runge-–Kutta time stage to suppress spurious oscillations. The OE procedure is defined by the solution operator of a damping equation, which can be analytically solved without requiring discretization, making its implementation straightforward, non-intrusive, and efficient. Through careful design of the damping coefficients, the proposed OEDG method not only achieves the essentially non-oscillatory (ENO) property without compromising accuracy but also preserves the conservative property—an indispensable aspect of the bound-preserving technique introduced in [J. Du and Y. Yang, J. Comput. Phys., 469 (2022), 111548]. The effectiveness and robustness of the OEDG method are demonstrated through a series of one- and two-dimensional numerical tests on the compressible Euler and Navier–Stokes equations for chemically reacting flows. These results highlight the method’s capability to handle complex flow dynamics while maintaining stability and high-order accuracy.