The 20-year-old, whose pace troubled the home side all afternoon, registered his first two goals for Rangers in just his third appearance with a pair of well-taken first-half strikes.
The home side made an encouraging start with some neat interplay pushing Rangers back in to their own half.
Perhaps the best chance for the Bluebirds early on fell to Jay Bothroyd but his drive was diverted wide by the outstretched leg of Mikele Leigertwood.
The visitors created their first real chance 10 minutes in when Akos Buzsaky found himself with time and space to line up a shot, but it was always rising and never really troubled home goalkeeper David Marshall who watched it over the bar.
A midfield battle ensued and chances became scarce. Midfielder Chris Burke and Bothroyd both tried their luck from distance - both were well wide.
But the opener arrived in the 19th minute when Simpson notched his first goal for the Rs.
Against the run of play defender Gary Borrowdale lofted the ball into the box and while the City defenders hesitated and appealed for the offside Simpson pounced to stab home a deflected Rowan Vine effort from close range.
Midfielder Peter Whittingham had a shot blocked by Ben Watson, while Joe Ledley fired a harmless effort straight into Radek Cerny's arms as the hosts tried to find an equaliser.
QPR's Simpson could and should have doubled his tally on the half-hour mark but skewed his shot wide of the left-hand post from a promising position.
But it did not matter as he helped himself to a second five minutes before the interval.
Wayne Routledge, who went racing down the right, threaded a neat little ball in behind the Bluebirds defence and Simpson, who came in on the angle, advanced towards goal before thumping the ball underneath Marshall.
It could easily have been three shortly after the interval but for Cardiff's Mark Kennedy, who cleared a Routledge shot off the line.
With 53 minutes gone Vine hit the post, curling the ball beyond Marshall who was relieved to see it come back off the woodwork.
Gavin Rae and Burke both had tame efforts dealt with by Cerny as Rangers were clearly happy to sit on their two-goal lead and absorb whatever the hosts could throw at them.
There were few clear cut chances in the closing stages but Burke was denied by Cerny, while Vine had a shot held by Marshall.
The impressive Simpson was withdrawn 13 minutes from time and the scoreline remained the same as the London club, who had only scored two goals on their travels until today, made it back-to-back wins on the road.