Ed de Goey's long goal kick was flicked on by Gifton Noel-Williams and, with defender Nicky Shorey, losing his footing, Peter Hoekstra was allowed to run into the box before rounding keeper Marcus Hahnemann and slotting the ball home.
Hahnemann redeemed himself slightly six minutes later when Darel Russell swept across him from the right to Noel-Williams at the back post but scrappy defending resulted in Lewis Neal receiving the ball.
However, the Reading shot-stopper saved at point-blank range.
The Potters added another before the break when Neal switched the play from right to left giving Hoekstra space to advance and strike a blistering shot from 25 yards at a tight angle into Hahnemann's top-right corner.
Reading looked more composed later on with the Royals managing to create a couple of chances. Kevin Watson went close when he smashed a low drive from the edge of the area but De Goey had it covered and watched it roll wide.
City completed their impressive victory when Shorey brought down man of the moment Hoekstra in the area to give away a penalty. The Dutchman subsequently stepped up to the spot to complete his hat-trick with a cheeky chip over the keeper.