The Bluebirds never recovered from a calamitous own goal in the sixth minute, Kevin McNaughton getting the fatal touch in a messy goalmouth scramble.
Joshua King combined with James Chester to heap further woe on Malky Mackay's men shortly after the break, with Aaron Mclean able to slot home a crucial third after seeing his initial shot repelled by David Marshall.
The swing in goal difference generated by Mclean's goal, coupled with Birmingham's defeat at Leicester, saw Nicky Barmby's charges end the evening in the final play-off place.
Cardiff contrived to gift their guests the lead with just six minutes played. Mark Hudson and McNaughton made a mess of a simple clearance, the latter bundling the ball beyond Marshall following a regulation corner from Andy Dawson.
Andrew Taylor and Kenny Miller threatened an instant response, combining well down the left flank to set up Joe Mason, but the young striker pulled up short after sprinting to reach the ball.
A momentary defensive lapse in the Hull backline allowed Miller to wriggled into space, but he slipped and scooped high and wide.
Cardiff were unable to carve regular openings in their opponents defence, though, and Mclean's pace on the break saw him well-placed to drive beyond Marshall's left post.
Barmby's men tidied up another Cardiff raid to free King down the right flank, but his centre lacked the required quality to meet Mclean, who was screaming for the ball.
Robert Koren then produced two solid efforts on goal for the visitors. First the Slovenian punted from fully 25 yards, Hudson blocking, before forcing Marshall into a catch at full stretch with a drive from similar range.
The home faithful were growing restless and suffered a further blow to their spirits as Cardiff had an equaliser chalked off in the 40th minute.
Miller was adjudged to have impeded goalkeeper Vito Mannone as he scrambled to nudge Peter Whittingham's inswinging corner over the line.
The disappointment grew after the interval, as the Tigers soon doubled their lead, King delivering a pinpoint centre for Chester to convert coolly from six yards.
Cardiff were quickly on the offensive as they searched to reduce the deficit, and only a brave block from Mclean denied Miller's angled drive towards Mannone's blind spot.
The missed opportunity proved costly for Mackay's men as the Tigers extended their lead further in the 55th minute.
This time, Mclean was the hero at the sharp end, seizing on Koren's through-ball to stab against Marshall and confidently turn home the rebound.
Miller rattled a post as the shellshocked Bluebirds scrambled to wrest back some control, but Koren nearly made it four as he struck hard and low at the under-siege Marshall.
Mackay brought on Robert Earnshaw for the frustrated Miller and he almost made an immediate impact, Mannone forced to tip a hard strike from the Wales international over the bar.
The hosts surged forward in search of a consolation as time ticked away at the Cardiff City Stadium, but Whittingham's wayward drive in the final minute summed up a night to forget for the Welsh club.
Source: PA