Methotrexate is an immunosuppressant that is generally the first drug prescribed to patient’s diagnosed with rheumatoid arthritis. By suppressing the immune system, inflammatory mediators causing inflammation of the synovium are produced in lower quantities. This leads to a reduction in the inflammation and subsequent reducing in pain.
Sulfasalazine is a free-radical scavenger. As neutrophils rely on free-radicals being present for activation, the removal of these reduces neutrophil activity and subsequently suppresses the immune response. This reduces the inflammation of the synovium and thus reduces the pain a patient experiences. The complete mechanism of action for sulfasalazine is not fully understood.
Both of these drugs are DMARDs, identified by chance, not design.