The home side started the better of the two teams, however it was the visitors who finished the stronger of the sides.
Rangers striker Kevin Gallen tested Neil Alexander with a shot after just five minutes, just moments after the visiting keeper turned aside Callam Willock's goal-bound header.
The Bluebirds eventually overcame Rangers' early promise and took the lead just before the hour mark when Earnshaw netted his first goal.
The diminutive hit-man continued his good early season form by effectively sealing the tie with a second just six minutes later.
Earnshaw completed his impressive hat-trick with a goal late on a low drive with minutes remaining. Substitute Andy Campbell, who replaced Earnshaw, gone in on the act himself by hitting a forth for the visitors.
City are now two points clear of second placed Wigan, who are at home to Northampton on Saturday, whilst Rangers are still clinging onto the final play-off spot in sixth.
Click here for Nationwide Division Two match stats:
Queens Park Rangers 0 Cardiff City 4
