The Bluebirds had to fight back from a goal down following Wilfried Zaha's early opener but two stunning goals from Peter Whittingham and Don Cowie got the job done.
The result means Malky Mackay's side will face West Ham in a two-legged play-off semi-final as they look to return to the top flight after a 50-year absence.
City, who may have had an eye on events at Vicarage Road, where seventh-placed Middlesbrough were in action against Watford, were quick out of the blocks and Liam Lawrence's early long-range drive was spilled by Lewis Price but he recovered in time to deny Joe Mason on the follow-up.
With 13 minutes gone Zaha silenced the sizeable away following with a goal right out of the top drawer. Picking up the ball in his own half, the 19-year-old laid it off for Darren Ambrose before darting upfield to receive a beautiful return pass which he coolly slotted past David Marshall.
With the Eagles buoyant, a clearly nervy Cardiff outfit struggled to find the form which had enabled them to remain unbeaten in the previous nine matches.
Mason's glancing header from Cowie's cross was easily dealt with by Price and the hosts looked relatively comfortable, working hard off the ball to contain their visitors while demonstrating an attacking threat in possession.
Cardiff's best chance of the half came five minutes before the break when Whittingham's quickly-taken free-kick caught Palace by surprise, allowing Mark Hudson to direct a header on goal against his former club but Price gathered at the second attempt.
With the Bluebirds needing victory to guarantee their place in the top six, they looked a different proposition in the second half. Kenny Miller fired off a shot within a minute of the restart to underline their intent, before the Scottish striker was booked for a dangerous tackle on Matthew Parsons.
When Parsons retorted with a foul of his own on Lawrence, earning himself a booking, Whittingham had the chance to deliver in a free-kick from a tight angle but went one better, finding the bottom corner to level the scores with his 13th goal of the season in the 53rd minute.
Moments later Miller flicked a header narrowly wide as Cardiff stepped up the pressure.
The shift in the balance of power was confirmed when Cowie, back in the side following a calf injury, struck a spectacular volley into the bottom corner after Gunnarson's throw had been flicked into the heart of the penalty area.
Palace were suddenly all at sea, lacking the fluency which had been the hallmark of their promising first-half display and appearing much more like a side on an eight-game winless run.
They did at least have the lively Zaha, whose 20-yard drive flashed just wide before a mazy dribble was brought to an end by Ben Turner's timely intervention.
Cardiff comfortably saw out three minutes of stoppage time to keep their promotion dream alive.