Stafford was fined $7,500 for throwing Moore to the ground. Moore, who was ejected following the fight, was docked $15,000.
The incident, in which Moore was blocking Stafford following an interception, sparked a lengthy fight in which players from both teams spilled on to the field.
Bears coach Lovie Smith said Monday that both players, Moore and Stafford, should have been ejected.
Friday's fines bring the total amount amount of fines from a particularly physical game to $62,500.