The 18-year-old was involved in all three goals before leaving the field with 40 minutes to go as managerless Gillingham's gloom deepened.
Jerome opened the scoring after 14 minutes after latching onto a Willie Boland through-ball to fire past Bertrand Bossu in the Gills goal. Bossu was a late replacement for Steve Banks who was injured during the pre-match warm-up.
Gillingham clawed their way back into the match after 33 minutes. City defender James Collins inexplicably headed the ball off his own post and failed to clear the subsequent corner, allowing Tommy Johnson to rifle home from six yards.
Cardiff were back in front before the break after Jerome was pulled down by Nyron Nosworthy in the Gillingham box.
Johnson was booked for his protests as the visitors felt Jerome had handled the ball but, Peter Thorne, making his first start for five weeks following neck trouble, coolly despatched the penalty to Bossu's right.
Cardiff started the second half brightly and Bossu reacted smartly to tip a Joe Ledley drive over the bar.
Thorne then found himself acres of space to seal the match on 55 minutes. Some clever link up play by Jerome and Jobi McAnuff led to the latter having a shot which cannoned off the unfortunate Danny Spiller right into a grateful Thorne's path.
Thorne should have then completed his hat-trick after 74 minutes but he blazed over from six yards.
Cardiff then introduced new loan signing Neil Harris in place of Jerome, who was given a standing ovation.
Gillingham chairman Paul Scally has promised to have a new manager in place by next weekend but the new man won't have any problem spotting Gillingham's problems on the evidence of the Kent club's second-half showing.