The Ladbrokes Premiership side, who will face Livingston in the next round, did not have it all their own way in the first half against the part-timers but broke the deadlock in the 17th minute with an exquisite goal from Jermain Defoe.
Ross Dunlop inadvertently turned the ball in his own net in the 57th minute to double Rangers' lead before Joe Aribo completed the scoring six minutes from time.
It was a satisfactory afternoon for visiting manager Steven Gerrard, who made 10 changes for the trip to Methil ahead of Thursday's Europa League play-off first leg in Poland against Legia Warsaw.
Glen Kamara was the only survivor from the 3-1 victory over Danish side Midtjylland three days earlier.
Despite the scale of the alterations, the Ibrox outfit wasted little time getting into their stride.
There were strong appeals for a penalty inside five minutes when Jordan Jones fell to the ground in the box as he raced clear of Stewart Murdoch but referee Don Robertson was not interested.
Defoe then found space inside the area but his low effort was comfortably saved by Jordan Hart.
After a bright start, however, Rangers went through a period of being careless in possession.
That gave the League One outfit confidence and Darren Young's side created a great chance after 17 minutes.
Liam Watt dug out a cross from the left that was missed by Rangers defender Andy Halliday as he challenged with striker Anton Dowds.
Aaron Dunsmore picked up the loose ball at the back post but goalkeeper Wes Foderingham spread himself well to make the block.
Rangers heaved a collective sigh of relief and stormed ahead six minutes later.
Defoe's sublime first touch took him away from Dunlop and Chris Higgins, having had his back to goal outside the box when he received debutant Filip Helander's pass, and the former England striker coolly placed a low shot past Hart from close range.
Rangers began the second half with designs of creating a two-goal cushion but Hart kept out Aribo's attempt at the near post after the midfielder connected with Jones' corner.
Defoe continued to pose problems inside the box but could only find the side-netting after wriggling free.
The second goal did arrive in the 57th minute courtesy of an own goal from East Fife defender Dunlop.
Jones nodded Greg Stewart's free-kick back across goal and Helander's glancing header struck Dunlop before landing in the net.
Rangers manager Gerrard freshened up his team on the hour mark by handing Brandon Barker and Andy King their debuts from the bench, the pair replacing Stewart and Greg Docherty.
Aribo grabbed the third and final goal six minutes from time, poking home a lose ball in the box after goalkeeper Hart flapped at Barker's corner.