Rangers were unfortunate not to open the scoring with five minuites on the clock when Lee McCulloch had a goal disallowed.
Kirk Broadfoot made a rare start for the Ibrox outfit and he swung in a ball from the right flank which was headed in by McCulloch. However, referee Crawford Allen spotted an infringment and the goal was disallowed.
East Stirling were well-organised and compossed on the ball in the opening quarter of the game. But three goals in the space of five minutes saw Rangers take control of the match.
McCulloch opened the scoring after 24 minuites with a fine finish. Charlie Adam lifted the ball into the area and McCulloch took it down before stepping inside Stephen Oates and firing the ball home from eight yards.
Kris Boyd almost doubled Rangers' lead 90 seconds later but the prolific frontman was denied by a fine save from East Stirling keeper Michael Brown.
However the third division club could only hold out for another 60 seconds as Alan Hutton netted Rangers' second goal. The full-back played a neat one-two with Alan Gow before drilling the ball low into the net.
Rangers rounded off an impressive five minutes' passage of play when Boyd netted their third goal. Gow provided his second assist of the evening as Boyd swept the ball into the net.
Just as the visitors looked set to hold out until the half-time interval, Rangers netted their fourth of the evening in first-half stoppage time.
Jean-Claude Darcheville did well down the left side before pulling the ball back to Boyd who netted his second goal.
McCulloch made it five at the start of the second half with a stunning strike. Adam laid the ball back to McCulloch who moved infield onto his right foot befor unleashing a stunning 25-yard strike that flew into the top corner of the net.
Thomas Buffel came on as a substitute on the hour mark, and he made an instant impact as he was tripped inside the area by Kevin McBride. Boyd converted from the spot to complete his hat-trick.
The 16-year-old John Fleck made his Rangers debut as a second-half substitute, and the youngster showed some neat touches in the closing 20 minutes, including a 20-yard strike that was deflected behind for a corner kick.