The catalytic activity of MOFs derives in a large extent from defects. To generate these defects, a cobalt-based metal–organic framework TMU-10, [Co6(oba)5(OH)2(H2O)2(DMF)4]n·2DMF has been subjected in the present study to controlled thermal treatment under air at different temperatures ranging from 100 to 700 °C. This treatment produces the removal of ligands, generation of structural defects, and additional porosity in an extent that depends on the conditions of the thermal treatment. The resulting defective materials, denoted according to the literature as quasi-MOFs, were subsequently employed as heterogeneous tandem catalysts in the one-pot synthesis of N-benzylideneaniline from aniline and benzyl alcohol in open air as a terminal oxidant at 60 °C under solvent-, base-, and dehydrating agent-free conditions. The quasi-TMU-10 framework obtained at 300 °C (QT-300) can efficiently promote imine synthesis within 2 h, forming water as the only byproduct. Unsaturated cobalt sites and the presence of micro- and mesopores in QT-300 are responsible for this excellent catalytic performance as tandem catalysts. The influence on QT-300 catalytic activity of catalyst amount, reactant ratio, and reaction temperature was investigated, as well as the stability and recyclability of the catalyst. The one-pot imine formation promoted by QT-300 follows alcohol aerobic oxidation and subsequent anaerobic condensation of the aldehyde intermediate with aniline.