The binding energies of the ground 1s²2s²2p_1/2 and first excited 1s²2s²2p_3/2 states in boronlike argon are rigorously evaluated. The calculations are performed by the QED perturbation theory in the framework of the extended Furry picture taking into account all the relevant first- and second-order radiative and correlation corrections. The third- and higher-order interelectronic-interaction effects are considered within the Breit approximation. The relativistic nuclear recoil effect is taken into account. In comparison with the previous calculations of the binding energies in boronlike argon the accuracy of the theoretical predictions has been significantly improved.