The Ibrox side netted four times after the break to extend their lead at the top of the table to five points.
Lee McCulloch opened the scoring from the penalty spot after 12 minutes and East Stirling were dealt a further blow when Phillipp Zufle was ordered off for a poorly-timed challenge on Kevin Kyle.
Andrew Little doubled Rangers' lead after 39 minutes, however the hosts replied just one minute later as Kevin Turner headed home Nathan Shepherd's corner.
But Lee Wallace re-established a two-goal advantage for Ally McCoist's side four minutes after the break before their lead was cut for the second time when Paul Quinn slotted home from the penalty spot.
Rangers were rewarded for their dominance throughout much of the second half when Kevin Kyle and Kai Naismith both netted to put the game well out of the reach of their opponents and McCulloch added a sixth goal eight minutes from time.