To generate purposely defects that can increase the catalytic activity, cobalt-based metal–organic framework (MOF) TMU-10 has been subjected to thermal treatment under an air atmosphere at temperatures between 100 and 700 °C. This process causes partial ligand removal, generating structural defects and additional hierarchical porosity in a convenient way. The resulting materials, denoted as quasi-MOFs, were subsequently employed as catalysts for the room-temperature borohydride reduction of 4-nitrophenol (4-NP). The quasi TMU-10 framework obtained at 300 °C (QT-300) exhibits excellent catalytic performance with an apparent rate constant, activity factor, and half-life time of 2.8 × 10–2 s– 1, 282 s–1 g–1, and 24.8 s, respectively, much better values than those of parent TMU-10. Coexistence of micro and mesopores, coordinatively unsaturated cobalt nodes, tetrahedral Co(II) ions, and Co(III) in QT-300 are responsible for this enhanced activity. Kinetic studies in the range of 25–40 °C varying the 4-NP and BH4– concentrations agree with the Langmuir–Hinshelwood model in which both reactants are adsorbed on the catalyst surface. Reduction of 4-NP by the surface-hydrogen species is the rate-determining step.