Land plants are continuously exposed to multiple abiotic stress factors like drought, heat, and salinity. Nitric oxide (NO) and hydrogen sulfide (H2S) are two well-examined signaling molecules that act as priming agents, regulating the response of plants to stressful conditions. Several chemical donors exist that provide plants with NO and H2S separately. NOSH is a remarkable novel donor as it can donate NO and H2S simultaneously to plants, while NOSH-aspirin additionally provides the pharmaceutical molecule acetylsalicylic acid. The current study aimed to investigate the potential synergistic effect of these molecules in drought-stressed Medicago sativa L. plants by following a pharmacological approach. Plants were initially pre-treated with both donors (NOSH and NOSH-aspirin) via foliar spraying, and were then subsequently exposed to a moderate water deficit while NO and H2S inhibitors (cPTIO and HA, respectively) were also employed. Phenotypic and physiological data showed that pre-treatment with NOSH synthetic compounds induced acclimation to subsequent drought stress and improved the recovery following rewatering. This was accompanied by modified reactive-oxygen and nitrogen-species signaling and metabolism, as well as attenuation of cellular damage, as evidenced by altered lipid peroxidation and proline accumulation levels. Furthermore, real-time RT-qPCR analysis revealed the differential regulation of multiple defense-related transcripts, including antioxidant enzymes. Overall, the present study proposed a novel role for NOSH compounds as efficient plant priming agents against environmental constraints through the coordinated regulation of multiple defense components, thus opening new horizons in the field of chemical priming research toward the use of target-selected compounds for stress tolerance enhancement.