City had Solomon Taiwo making his first start in place of the suspended Stephen McPhail. Gavin Rae had to be content with a place on the bench.
Wayne Routledge was in the Rangers line-up alongside a former City target in striker Rowan Vine.
City used the flanks in the opening minutes and Peter Whittingham and Chris Burke saw plenty of the ball, but it was Rangers who had the first strike on goal when Akos Buzsaky fired over in the 10th minute from just outside the area.
Rangers took the lead in controversial fashion, when Simpson appeared to be offside when he gathered the ball from Vine in the 19th minute to slot beyond David Marshall from a central position.
Simpson could have doubled the lead on the half hour, but he dragged his shot across the face of the goal with only Marshall to beat.
Rangers doubled their lead five minutes from the interval when Routledge split a hesitant Bluebirds defence with a pass out to the unmarked Simpson, who drove a low angled shot into the net.
No changes after the interval were surprising as the Bluebirds had hardly looked like a side in fourth place in the division.
The pattern of play remained the same as Rangers penned the Bluebirds back in defence and a mistake by Taiwo let Vine in on goal, but his shot struck the upright with Marshall beaten.
City boss Dave Jones made changes in the 54th minute with Rae and Josh Magennis replacing Taiwo and Whittingham.
The disappointing Jay Bothroyd made way for Ricky Scimeca in the 67th minute as Jones made his last play to get back into the match.
The Bluebirds were more of an attacking threat in the closing quarter, but without troubling the visitors' goal and Rangers fully deserved their victory.