Cardiff missed the chance to secure a place in the play-offs after Luciano Becchio's equaliser for Leeds.
The striker glanced home a header after Paul Connolly's determined chase saw him pull the ball back for Becchio.
Joe Mason had put Cardiff ahead when he collected a raking crossfield pass and lifted his shot over Andy Lonergan.
Lonergan went on to deny Kenny Miller and Andrew Taylor with top-class saves to keep Leeds in it, although they had Leigh Bromby carried off injured.
The defender appeared to catch his studs in the turf midway through the first half and crumpled in agony, receiving oxygen before medical staff called for a stretcher.
A victory for Cardiff would have seen the Bluebirds guarantee their place in the play-offs.
And nearest challengers Middlesbrough later beat high-flying Southampton 2-1, leaving Cardiff unable to start planning for post-regular season football.
Cardiff, unbeaten now in their last nine matches - albeit with six draws - now face a nerve-jangling last-day finale at Crystal Palace in their bid to make it a hat-trick of top-six finishes.
Bluebirds midfielder Liam Lawrence had an early effort saved by Leeds goalkeeper Lonergan, and at the other end Ross McCormack headed wide against his former club after good work from Robert Snodgrass.
Mason skewed his close-range effort off target as Cardiff sought an early breakthrough, but neither side created a further chance before Leeds defender Bromby was carried off in the 32nd minute.
Bromby, who appeared to slip awkwardly unopposed and required immediate medical attention, was replaced by Paul Connolly.
That setback appeared to distract the visitors and Cardiff caught them napping to take the lead four minutes before the break.
Mason, who this week signed a new four-year deal with Cardiff, raced on to Peter Whittingham's long pass from inside his own half and held his nerve to lob the ball over the advancing Lonergan from inside the penalty area.
City striker Miller was then denied in fine style by Lonergan, who kept out the Scot's angled 18-yard drive as Cardiff threatened to increase their lead in time added on at the end of the first half.
Leeds began the second half with renewed purpose. Thompson's fierce shot was blocked by Cardiff defender Ben Turner and Becchio headed wide from 12 yards soon after.
Leeds boss Neil Warnock sent on Ramon Nunez and Danny Webber for McCormack and Adam Clayton respectively just before the hour-mark and the visitors then went close when Danny Pugh's 20-yard effort flew wide.
The visitors continued to give as good as they got, but Lonergan was forced into another excellent save in the 70th minute when keeping out Taylor's goal-bound volley.
Leeds then dealt Cardiff's play-off hopes a blow with the equaliser three minutes later. Substitute Connolly swung over a fine cross from the right and Becchio rose above the home defence to head beyond Cardiff goalkeeper David Marshall into the bottom corner.
Cardiff substitute Filip Kiss fired wide from the edge of the area and Whittingham failed to keep his 87th-minute free-kick on target as Leeds held on for a deserved point.