Band structure engineering of large band gap perovskite oxides allows enhancing their optical absorption capabilities in the visible region of the electromagnetic spectrum which enables their use in green energy technologies harnessing solar radiations. Since introducing isovalent cation and anion co-dopants in ABO3 perovskite can facilitate tuning of their band gaps, in the present work we examine the synthesis feasibility of Ti and X (where X = S, Se and Te) dopants at zirconium and oxygen-sites, respectively, of BaZrO3 using first-principles density functional theory calculations. For an accurate determination of thermodynamic, structural and energetic properties of the pristine, mono-doped and TiZr + XO co-doped BaZrO3, we have employed semi-local SCAN meta-GGA functional. Moreover, the TB-mBJ meta-GGA potential functional was used to circumvent the band gap underestimation of the electronic and optical properties made by SCAN. Our results indicate that introducing TiZr as a co-dopant in XO-doped BaZrO3 not only improves the thermodynamics of introducing an chalcogen atom at oxygen-site under optimal chemical environment, it also allows tuning the band gap of cubic BaZrO3 for absorption of radiation in the visible spectrum. We also perform a side-by-side comparison of the photocatalytic water molecule dissociation efficiency of pristine, XO-doped, TiZr-doped and TiZr +XO co-doped BaZrO3 to examine their potential application in hydrogen evolution process. Based on our computed optical properties and band-edge potentials, we propose TiZr+TeO co-doped BaZrO3 as the best candidate for photocatalytic water molecule dissociation under solar irradiation.