The home side tested Cammy Bell with a couple of half-chances inside the opening 20 minutes, but the league leaders soon started to dominate.
Lee Wallace came close to opening the scoring when he struck the crossbar with just over half an hour played.
However, Law was able to give Rangers the lead two minutes later, tapping in from a Richard Foster cross.
The first half ended on a sour note for the visitors, as Arnold Peralta was shown a straight red for a dangerous high challenge.
Stenhousemuir keeper Chris Smith continued to be tested in the second period as Rangers rarely gave their hosts a chance, despite being a man down.
Their persistence paid off late on as Law managed to double their lead in stoppage time with well-struck half-volley, sealing the win for Rangers in the process.