The Wee Rangers famously defeated the Glasgow giants in the Scottish Cup back in 1967 but the class of 2013 were unable to repeat the feat in this second round clash at Ibrox.
Rangers made three changes from the side who romped to a 6-0 win at Airdrie in the Scottish League One on Friday.
Emilson Cribari returned from injury to take his place in the heart of defence, while David Templeton and Dean Shiels were added to the side.
With trialists not permitted beyond the first round, new recruits Jon Daly and Nicky Law were ineligible - as Rangers await the end of a transfer embargo on September 1 - while Kyle McAusland was dropped to the bench.
Despite still naming a strong side, it took some time for Rangers to get going and convert their possession into chances in front of goal.
Little tested the goalkeeper when he raced onto a Lee Wallace pass from the left flank and drew a save at the near post from Paul Grant.
Cribari then came close when he met a corner with a downward header that bounced off the turf and over the crossbar.
The home side should have been ahead when Lewis Macleod released Little into the box for a shot that lacked power but looked set to trickle over the line until Michael Dunlop hooked to safety at the last second.
It proved to be the only real moment of excitement in a drab and uninspiring first half, as a combination of slack passing and poor finishing from Rangers saw them head into half-time still searching for the opener.
The breakthrough almost came three minutes after the restart when Sebastien Faure's impressive volley was just tipped over the crossbar by Grant.
With the tie still deadlocked after an hour, McKay was thrown into the action for Shiels and had an immediate impact when he netted with his first touch of the ball less than a minute later.
Little supplied the pass and McKay produced a fine angled drive into the bottom corner before Rangers struck again on 62 minutes.
This time, Little found the net when he rose to meet a Robbie Crawford cross and send a bullet header beyond Grant to double the advantage and secure Rangers' progression in the competition.