Light Blues boss Ally McCoist rested a number of players for the quarter-final, but his side still progressed with goals in either half from Jon Daly and Ian Black at New Bay View.
Daly was handed a starting role in the Gers attack alongside Nicky Clark and the pair seized their chance to impress, combining well for the opening goal in the 29th minute. Clark forced his way into the box and his inviting low cross was bundled in off the post by Daly.
Rangers were denied a second goal before the break when Lee McCulloch’s close-range finish was ruled out for offside.
But McCoist’s men struck again in the second period as a fierce free-kick from Black found the net in the 57th minute, despite Allan Fleming getting a glove to the ball.
The Fifers nearly conceded a third when Fraser Aird’s cross clipped the bar, but Rangers had already done enough to secure a semi-final clash with Alloa.