The criticality-enhanced magnetocaloric effect (MCE) near a field-induced quantum critical point (QCP) in the spin systems constitutes a very promising and highly tunable alternative to conventional adiabatic demagne- tization refrigeration. Strong fluctuations in the low-T quantum critical regime can give rise to a large thermal entropy change and thus significant cooling effect when approaching the QCP. In this work, through efficient and accurate many-body calculations, we show there exists a significant inverse MCE (iMCE) in the spin-1 quantum chainmaterials(CH3)4NNi(NO2)3 (TMNIN)andNiCl2-4SC(NH2)2 (DTN),whereDTNhassubstantiallow-T refrigeration capacity while requiring only moderate magnetic fields. The iMCE characteristics, including the adiabatic temperature change Tad, isothermal entropy change S, differential Grüneisen parameter, and the entropy change rate, are obtained with quantum many-body calculations at finite temperature. The cooling performance, i.e., the efficiency factor and hold time, of the two compounds is also discussed. Based on the many-body calculations on realistic models for the spin-chain materials, we conclude that the compound DTN constitutes a very promising and highly efficient quantum magnetic coolant with pronounced iMCE properties. We advocate that such quantum magnets can be used in cryofree refrigeration for space applications and quantum computing environments.