Kevin Watt pulled a goal back for the hosts early in the second half but the destination of the three points was never really in doubt.
Having initially struggled with games on the road in the Irn-Bru Third Division this season, Broadwood was the scene of Rangers' first away win in the league in October.
Today's win at the same venue signalled their eighth successive victory on their travels.
Rangers named an unchanged side following last week's impressive 4-0 victory over Queen's Park for the clash with the Bully Wee.
With skipper Lee McCulloch, Francisco Sandaza and Kevin Kyle all still injured, and Kal Naismith suspended, Little was again tasked with leading the line after grabbing a double against the Spiders.
And the Northern Irishman needed just eight minutes to find the back of the net again against Clyde.
Little played the ball out to Dean Shiels on the right before bursting into the box to collect the return pass and all that was required was a simple finish past goalkeeper Jamie Barclay.
The visitors were threatening again when Templeton swung a teasing corner into the goal-mouth and Ian Black who opened his goal-scoring account for the club last week nodded just over.
Instead, it was Little who grabbed his second of the day with 25 minutes on the clock. This time he raced onto a Kyle Hutton pass, before turning marker Iain Gray and lashing high into the net.
There was some last-gasp defending required from Clyde when Ryan MacBeth cleared an Emilson Cribari flick off the line.
But the home side found themselves trailing further a minute before the break when Templeton tried his luck with a superb 30-yard strike that cracked off the inside of the post and over the line.
The Bully Wee threw themselves a life-line three minutes after the restart when Stuart McColm whipped into the path of Watt and he stabbed home at the front post.
The home fans then claimed for a penalty for a Chris Hegarty barge on Stefan McCluskey but there was no award from referee Kevin Clancy.
At the other end, only a great save from Barclay prevented Hegarty's close-range header from finding the back of the net.
Templeton struck again 10 minutes into the second half with another impressive goal - and his 11th of the season for Rangers.
The winger demonstrated some lovely movement as he surged into the box from the left before dispatching into the far corner from a tight angle.
Both Little and Templeton were now chasing hat-tricks but it was Hutton who was not too far away with a low drive that flashed just past the upright.
Templeton made way for Fraser Aird and the teenager - who penned a new five-year deal this week - saw his thunderous effort fizz just wide of target.