The striker – on loan from Stoke City – opened his account for the Selhurst Park club with a headed effort six minutes in.
Marouane Chamakh then scored his second goal in as many matches to double the hosts' lead after the interval, as Palace's resurgence under new manager Tony Pulis continued.
The result gives Palace their first back-to-back league victories of the season, while Cardiff are winless in five.
Pulis made no changes to the Palace side that beat West Ham 1-0 on Tuesday, with former Cardiff duo Danny Gabbidon and Jerome included in his starting XI.
Kim Bo-Kyung came in for Aron Gunnarsson in the visitors' only alteration from Wednesday's goalless draw at Stoke.
Cardiff were quick out of the blocks as an unmarked Fraizer Campbell got his head to a Don Cowie cross from the right in the second minute, but should have done better as Julian Speroni pushed the ball behind for a corner.
However, it was Palace who broke the deadlock four minutes later, with Jerome netting against the club he spent two seasons with between 2004 and 2006.
Jason Puncheon chipped the ball into the six-yard box and Jerome sent a downward header beyond a flailing David Marshall, ending his 21-game goal drought.
Palace continued to put pressure on the Cardiff defence, with Barry Bannan sending an effort high and wide of the target from the edge of the penalty area as he aimed to double his side's tally.
As Cardiff struggled to cope with the hosts' high-tempo start, Gary Medel drilled a shot from distance wide of the right-hand post in the 29th minute.
Joel Ward stormed forwards on the stroke of half-time, exchanging passes brilliantly with Mile Jedinak, but his eventual effort was deflected wide for a corner.
Palace continued to look threatening after the break, with Puncheon driving wide of the right-hand upright from 25 yards three minutes into the second period.
Jerome then forced Marshall into a diving save – his low driven effort tipped around the post by the Scot.
But the Palace pressure paid off as Chamakh doubled the home advantage in the 57th minute, when Ben Turner's attempted clearance fell kindly for the Moroccan, who fired a right-footed shot into the bottom right-hand corner of the net.
Goal-line technology was put to the test in the 69th minute as Marshall scrambled a Jerome header off the line, with replays suggesting the majority of the ball had crossed the line, although not enough to make it 3-0.
Jerome's inspired performance continued as he directed a left-footed strike narrowly wide of the target 10 minutes from time, while his former employers barely threatened as they left London empty-handed.
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