Rheumatoid arthritis (RA) is a chronic immune-related condition, primarily of joints, and is highly disabling and painful. The inhibition of Janus kinase (JAK)-related cytokine signaling pathways using small molecules is prevalent nowadays. The JAK family belongs to nonreceptor cytoplasmic protein tyrosine kinases (PTKs), including JAK1, JAK2, JAK3, and TYK2 (tyrosine kinase 2). JAK1 has received significant attention after being identified as a promising target for developing anti-RA therapeutics. Currently, no crystal structure is available for JAK1 in complex with the next-generation anti-RA drugs. In the current study, we investigated the mechanism of binding of baricitinib, filgotinib, itacitinib, and upadacitinib to JAK1 using a combined method of molecular docking, molecular dynamics simulation, and binding free energy calculation via the molecular mechanics Poisson-Boltzmann surface area (MM-PBSA) scheme. We found that the calculated binding affinity decreases in the order upadacitinib > itacitinib > filgotinib > baricitinib. Due to the increased favorable intermolecular electrostatic contribution, upadacitinib is more selective to JAK1 compared to the other three inhibitors. The cross-correlation and principal component analyses showed that different inhibitor bindings significantly affect the binding site dynamics of JAK1. Furthermore, our studies indicated that the hydrophobic residues and hydrogen bonds from the hinge region (Glu957 and Leu959) of JAK1 played an essential role in stabilizing the inhibitors. Protein structural network analysis reveals that the total number of links and hubs in JAK1/baricitinib (354, 48) is more significant than those in apo (328, 40) and the other three complexes. The JAK1/baricitinib complex shows the highest probability of the highest-ranked community, indicating a compact network of the JAK1/baricitinib complex, consistent with its higher stability than the rest of the four systems. Overall, our study may be crucial for the rational design of JAK1-selective inhibitors with better affinity.