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It took the visitors just eight minutes to break the deadlock, Little firing in from a Dean Shiels pass.
The 23-year-old added his second in the 24th minute, easily beating the Clyde defence after picking up the ball from Kyle Hutton.
Templeton ensured that Rangers had a three-goal advantage at half time, as he blasted the ball in from 30 yards.
Kevin Watt got a goal back for the hosts shortly after the restart, but Templeton soon found his second to restore the three-goal cushion.
Shiels and Fraser Aird both had chances to add a fifth for the league leaders, but they could not find the back of the net.
The win ensures that Rangers remain 22 points ahead of Queens Park in the league table.