The aptly named Andrew Stirling gave the visitors the half-time lead but two goals from Andrew Little and one from the prolific Lee McCulloch saw Ally McCoist's side safely home.
The home side dominated the opening stages, with Little heavily involved as he saw a low shot saved by 19-year-old goalkeeper Grant Hay before he headed over after David Templeton's delivery slipped off the top of his head.
Rangers showed a few nerves in defence but they continued to press forward, with Hay again keeping out a powerful Lee Wallace effort.
Kal Naismith then spurned two half-chances but East Stirling looked tidy in possession and went close with a neat move down the right, although no one was on hand in the box to convert a short pass from Michael Hunter following good work from Paul Quinn.
East Stirling then took the lead following another well-worked move, with Stirling receiving the ball back courtesy of a cheeky flick round the corner from Quinn before letting the ball bounce and slotting home (40).
Hay was called upon to ensure his side held the lead at the break as he palmed away a drilled 20-yard free-kick from McCulloch, with Chris Hegarty unable to convert the rebound.
Rangers players left the pitch at the break with boos ringing in their ears but they responded in positive fashion, with Little drawing them level on 51 minutes.
Anestis Argyriou picked Little out in the middle following a determined run forward and the striker got ahead of marker James Glasgow to slot home.
Two goals in as many minutes then killed the contest off, McCulloch grabbing the first when he rounded the keeper and calmly slotted home after Templeton had fed the ball through to him (62).
Rangers' third goal was all down to the persistence of Little, who dispossessed right-back Nathan Shephard near the halfway line before driving into the penalty area and slotting home.
The visitors briefly threatened but Stirling could not get on the end of a cross from Scott Maxwell and instead it was left to the impressive Hay to keep the score down, the keeper keeping out a deflected McCulloch drive before retrieving the ball as it came back off the upright.
McCoist's charges had one final chance of note in the closing stages, McCulloch heading just past the post after getting on the end of a precise cross from substitute Barrie McKay, but the miss proved to be academic.