Myeloid cell leukemia-1 (Mcl1) is an anti–apoptotic protein that has gained considerable attention due to its overexpression activity prevents cell death. Therefore, a potential inhibitor that specifically targets Mcl1 with higher binding affinity is necessary. Recently, a series of N-substituted 1-hydroxy-4-sulfamoyl-2-naphthoate compounds was reported that targets Mcl1, but its binding mechanism remains unexplored. Here, we attempted to explore the molecular mechanism of binding to Mcl1 using advanced computational approaches: pharmacophore-based 3D-QSAR, docking, and MD simulation. The selected pharmacophore—NNRRR—yielded a statistically significant 3D-QSAR model containing high confidence scores (R2 = 0.9209, Q2 = 0.8459, and RMSE = 0.3473). The contour maps—comprising hydrogen bond donor, hydrophobic, negative ionic and electron withdrawal effects—from our 3D-QSAR model identified the favorable regions crucial for maximum activity. Furthermore, the external validation of the selected model using enrichment and decoys analysis reveals a high predictive power. Also, the screening capacity of the selected model had scores of 0.94, 0.90, and 8.26 from ROC, AUC, and RIE analysis, respectively. The molecular docking of the highly active compound—C40; 4-(N-benzyl-N-(4-(4-chloro-3,5-dimethylphenoxy) phenyl) sulfamoyl)-1-hydroxy-2-naphthoate—predicted the low-energy conformational pose, and the MD simulation revealed crucial details responsible for the molecular mechanism of binding with Mcl1.