The winger set up Lee Wallace for the opener, before grabbing a lovely goal of his own.
Substitute Dean Shiels then put the gloss on the Glasgow giants' ninth win in a row, as they moved 12 points clear at the top of the table.
Rangers made one change from the side who defeated Elgin City at the weekend, with Ross Perry drafted into the starting line-up and Anestis Argyriou missing out with a knock.
Clyde tried their luck early on when Kevin Watt surged into the box from the left before unleashing a shot that fell well over the crossbar and did little to trouble Neil Alexander.
At the other end, Bully Wee goalkeeper Jamie Barclay was called into action to make a decent save from a thunderous Lee McCulloch strike.
Wallace then slotted into the path of Lewis Macleod, who cut across the face of goal for Andy Little but he connected awkwardly and the chance was lost.
Rangers continued to press for the opener and a McCulloch cut-back found Templeton but his powerful strike from distance was straight at Barclay and easily smothered.
However, the Clyde goalkeeper was unable to prevent the home side from opening the scoring with 21 minutes gone.
Wallace raced on to a Templeton pass before bearing down on goal and slotting between the legs of Barclay and into the back of the net.
Rangers manager Ally McCoist was forced to make a change seven minutes later when Little limped out of the action and was replaced by Shiels, who missed the last two games through injury.
Rangers went in search of a second goal and a sequence of neat passes ended with Kyle Hutton's 25-yard effort fizzing inches past the upright.
Hutton had to settle for being the provider instead as the Light Blues doubled their lead in style after 38 minutes.
Templeton collected from the midfielder and demonstrated excellent control to skip past his marker before curling past the grasp of Barclay with a superb finish.
McCulloch had the net bulging two minutes later after dinking over the keeper but he was denied a goal of his own by the offside flag.
Rangers continued to dominate after the restart and Barrie McKay set up Hutton for a shot that squeezed past several bodies in the box before Barclay gathered.
McKay then teed up a shot for Templeton but he failed to add to his tally with a strike that cannoned off the body of Gavin Brown and out for a corner.
Hopes of a Clyde comeback were shattered when Rangers claimed their third of the day after 76 minutes.
McKay delivered the pass to the feet of Shiels, who turned and dispatched a low drive into the far bottom corner to secure the points.
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