Inflammation involves a complex biological response of the body tissues to damaging stimuli. When dysregulated, inflammation led by biomolecular mediators such as caspase-1 and tumor necrosis factor-alpha (TNF-alpha) can play a detrimental role in the progression of different medical conditions such as cancer, neurological disorders, autoimmune diseases, and cytokine storms caused by viral infections such as COVID-19. Computational approaches can accelerate the search for dual-target drugs able to simultaneously inhibit the aforementioned proteins, enabling the discovery of wide-spectrum anti-inflammatory agents. This work reports the first multicondition model based on quantitative structure–activity relationships and a multilayer perceptron neural network (mtc-QSAR-MLP) for the virtual screening of agency-regulated chemicals as versatile anti-inflammatory therapeutics. The mtc-QSAR-MLP model displayed accuracy higher than 88%, and was interpreted from a physicochemical and structural point of view. When using the mtc-QSAR-MLP model as a virtual screening tool, we could identify several agency-regulated chemicals as dual inhibitors of caspase-1 and TNF-alpha, and the experimental information later retrieved from the scientific literature converged with our computational results. This study supports the capabilities of our mtc-QSAR-MLP model in anti-inflammatory therapy with direct applications to current health issues such as the COVID-19 pandemic.