Robert Snodgrass struck a second-half equaliser for Leeds after an inspired performance by keeper David Marshall had threatened to deny the hosts.
Cardiff took a 17th-minute lead when Joe Mason pounced on Darren O'Dea's hesitancy for an opportunist strike.
Leeds completely dominated from then on as Snodgrass, Ross McCormack and Adam Clayton tested Marshall.
But the goalkeeper had no chance when Snodgrass poked in from Tom Lees' knock-down 17 minutes from time.
Lees then wasted a glorious chance to snatch victory in the closing stages but he failed to connect properly with a free header from six yards.
Cardiff, who have now failed to win in six consecutive away games, could have had few complaints had Lees scored after the visitors offered almost nothing as an attacking force in the second half.
The result ends a string of six straight defeats for Leeds against the Bluebirds, but the home side created enough opportunities to feel they deserved better.
Cardiff's opener owed much to Mason's perseverance but O'Dea's dithering just inside his own penalty box was the deciding factor.
The centre-back won the race to Peter Whittingham's speculative through ball, but he stumbled as he attempted to clear, giving Mason the opportunity to nick the ball.
Mason, whose fine recent form kept Kenny Miller and Rob Earnshaw on the bench, shifted the ball to his left to avoid Rachubka's lunge and finished left-footed at full stretch for his third goal in as many games.
O'Dea could point to a slight nudge from behind as he reached the ball, but it was his own indecision that opened the door for Mason.
Leeds responded positively, and both Andy Keogh and McCormack were inches away from connecting with Paul Connolly's superb low cross behind Cardiff's static back four.
Keogh's earlier header had forced Marshall into a point-blank save, and then the keeper got down well to turn Snodgrass' header around the post.
The home side then took full control after the break as they added much needed impetus into their play, but they found Marshall on top form.
Snodgrass fired a thunderous drive straight at the Scotsman, before McCormack's low curler forced the keeper to dive low to his left.
Adam Clayton was the next to try his luck - his first effort, a 30-yard drive, was tipped over, and a desperate block from a Cardiff defender then spared Marshall from having to stop his fierce volley.
From the resulting corner, Marshall produced the save of the match as he threw out a strong left hand to stop Jonathan Howson's downward header.
But the incessant Leeds pressure finally brought the deserved equaliser on 73 minutes as Snodgrass ended Marshall's impressive resistance.
Lees rose highest to meet a hopeful ball into the Bluebirds box and Snodgrass poked the ball home as Marshall chose to stay on his line.
Cardiff were lucky to escape when Lees' glancing header went inches wide, but the home side were indebted to Aidy White in the final minute as he cleared from under his own bar as Aron Gunnarsson looked to pounce.
Leeds United manager Simon Grayson: "When you look at the chances we created and the number of top saves their keeper made, we can feel unfortunate not to win the game.
"We didn't start as brightly as we could, and we had to up the tempo after half-time.
"But we found their keeper in inspired form and, on another day, we could have won."
Cardiff City manager Malky Mackay: "Leeds had a lot of pressure in the second half but I thought controlled the game in the first half.
"We created a couple of chances near the end as well where could have nicked the win so overall I think a draw was a fair result.
"We played well in that first half and we were playing against a team who have had one defeat at home this season."