Jon Daly found the net as Rangers lead East Fife by a goal to nil in their Petrofac Training Cup quarter-final at East Fife.
The Gers came close to an opener in the 12th minute when Daly nodded Fraser Aird's cross on to David Templeton, and the winger forced an impressive save out of Allan Fleming in the Fifers goal.
Ally McCoist's side edged their noses in front in the 29th minute through Daly, who was on hand to bundle the ball over the line after Nicky Clark picked him out with a deft cross.
Rangers are 45 minutes away from setting up a semi-final clash with Alloa Athletic.
