Captain Lewis Wing put the Royals ahead on 38 minutes with an excellent long-range strike, which was his third of the season, and his first since scoring against his old club Wycombe back in August.
Noel Hunt’s men went into the break a goal up, an Omari Kellyman finish of 49 minutes, and a Yousef Salech goal just after the hour mark, gave the Bluebirds all three points.
The result means Cardiff are now top of the League One table with 26 points from their opening 12 games, whilst Reading are third bottom, with just two wins in 12.
Up next for the Select Car Leasing outfit is Northampton Town at home on October 21.