Ally McCoist’s side notched their third victory of the season over their local rivals as Andy Little and David Templeton both netted twice.
Little took only eight minutes to open the scoring with his 19th goal of the season – a neat finish from Dean Shiels’ superb pass.
Templeton then attempted a cheeky chip over Clyde goalkeeper Jamie Barclay and Ian Black headed over as Rangers remained in command.
The second goal arrived in the 24th minute when Little strolled through the home defence and rifled in a shot after being played in by Kyle Hutton.
There was then some last-gasp defending required from Clyde when Ryan MacBeth cleared an Emilson Cribari flick off the line.
Rangers goalkeeper Neil Alexander easily gathered John Sweeney’s free-kick in a rare Clyde attempt on goal but the visitors made it 3-0 in style in the 44th minute with Templeton smashing home a shot from fully 30 yards out.
The one-way traffic continued after the restart with Little blazing over, but the hosts pulled a goal back in the 47th minute when Kevin Watt converted Stuart McColm’s teasing cross from close range.
There was to be no surprise comeback though as Templeton doubled his tally in the 54th minute with another stunning goal as he waltzed through the Clyde defence before finding the net.
Rangers continued to dominate but were unable to add a fifth goal with Cribari, Hutton, Shiels and substitute Fraser Aird all spurning chances.