There is a trade-off between the sparseness of an absorber array and its sound absorption imposed by wave physics. Here, near-perfect absorption (99% absorption) is demonstrated when the spatial period of monopole-dipole resonators is close to one working wavelength (95% of the wavelength). The condition for perfect absorption is to render degenerate monopole-dipole resonators critically coupled. Frequency domain simulations, eigenfrequency simulations, and the coupled mode theory are utilized to demonstrate the acoustic performances and the underlying physics. The sparse-resonator-based sound absorber could greatly benefit noise control with air flow and this study could also have implications for electromagnetic wave absorbers.