Stoke fell behind after only ten minutes when a comical display of defending allowed Joe Ledley to slip a ball through for Jerome who coolly slotted into Steve Simonsen's bottom left corner.
A second followed only two minutes later when a 30-yard Jason Koumas free-kick was met by a crowd of heads but Darren Purse climbed the highest to flick past the helpless goalkeeper.
Luke Chadwick's darting run inside the area looked to have given Stoke a way back when he was brought to ground by a Rhys Weston tackle, but the referee turned down any penalty shouts.
More slack defending by the home team in the 43rd minute was punished when Ledley threaded the ball for Jerome once again who simply sidestepped Simonsen and slotted in an empty net from 14 yards.
Stoke were unlucky not to claw a goal back seven minutes after the break when Paul Gallagher's 20-yard free-kick crashed back off Neil Alexander's crossbar.
Gallagher continued to plug away but to no avail when he attempted a 25-yard drive but his shot never troubled Neil Alexander, clearing the crossbar.
In search of his hat-trick, Jerome pounced on a failed back pass by Junior, but after touching the ball too far the striker went looking for a penalty with a theatrical dive that gained him a booking.
Substitute Paul Parry almost furthered his side's massive lead on 81 minutes when his drive across the face of goal had to be turned around the post by the slightest touch of Simonsen's glove.
The addition of Martin Kolar in the 84th minute proved too little, too late as the Bluebirds claimed their third win in four games.