Palace made the trip north for this one despite a host of postponements locally because of the undersoil heating at Elland Road and a great effort by the locals in clearing the heavy snowfall in surrounding areas of the stadium.
George Burley was once again without the suspended Owen Garvan and injured skipper Paddy McCarthy but also suffered the loss of Alex Marrow who missed the game with an ankle injury. The home side made one change to their side with suspended Paul Connolly missing out with Andrew Hughes coming into the starting eleven.
The United supporters had early celebrations cut short when they thought they had taken the lead but a flag raised for offside came to Palace's rescue. Jonny Howson picked up a long ball from the Max Gradel and made no mistake with the finish but the assistant referee raised his flag and the deadlock hadn't been broken.
Leeds had the better of the early exchanges in the half and Bradley Johnson saw his free kick deflected wide off a defender and then Robert Snodgrass saw his shot blocked by Anthony Gardner.
Julian Speroni denied Howson and Johnson saw another shot blocked as the pressure continued but it was six minutes before the break when the best chance came their way.
Snodgrass played the ball back into the path of Luciano Becchio but he couldn't get hold of the ball properly and it was left to Gradel to shoot but he put his shot wide of the target.
After defending so well in the half it was the visitors who went into the break with the lead. Some great work by Nathaniel Clyne down the wing ended with him putting over the perfect cross for Neil Danns to break the deadlock right on forty five minutes.
Palace nearly extended their advantage in added time of the first half when Kasper Schmeichel had to tip a free kick by Darren Ambrose from 25 yards out over his bar.
The second half soon saw changes by the Leeds management with both Lloyd Sam and Ross McCormack coming on to try and force their side back into the game.
On 47 minutes Sam was soon involved as his work set up Neil Kilkenny for a shot from 25 yards out but Speroni made the save.
Just past the hour mark the 'keeper was called upon again as Snodgrass put the cross in and Luciano Becchio met it with a header but an excellent save kept Palace ahead.
Palace themselves always looked for chances to extend their lead. A James Vaughan shot at goal was blocked by Andrew O Brien and then on 71 minutes Danns had a good chance for another but his shot this time struck a post.
Substitute Sam saw the best of Speroni to deny him as the keeper turned his shot around the post but was then beaten only for the flag to once again come to Palace's rescue.
McCormack's effort ruled out but the home side were soon made a further change from the bench and with it more chances.
Billy Paynter came on for Hughes and was soon having a say in affairs.
He got on the end of a cross from Kilkenny to find Luciano Becchio whose left footed shot put United on level terms with nine minutes remaining.
After holding the lead from just before the break it was just a couple of minutes and the visitors found themselves behind.
The ball was picked up by Becchio and he ran on and fired the winner past Speroni who had no chance with this one and the whole atmosphere in the stadium had changed.
Burley made one late change as Wilfried Zaha came on for N'Diaye as his side tried to get something from the game.
In four minutes of added time that equaliser couldn't be found while at the other end Speroni denied Paynter from extending the advantage.
Leeds United: Schmeichel, Hughes (Paynter 76), Bruce, O'Brien, McCartney, Kilkenny, Johnson (Sam 55), Snodgrass, Howson, Gradel (McCormack 54),Becchio.
Subs: Higgs, Collins,Faye, Somma.
Booked : Snodgrass, Gradel, Johnson, Becchio.
Crystal Palace: Speroni, Clyne, Davis, Gardner, Wright, Ambrose, Danns, N'Diaye (Zaha 86), Djilali (O'Keefe 54), Vaughan, Counago.
Subs: Barrett, Cadogan, Obika, Dorman, Price.
Booked : Wright, O'Keefe.
Attendance : 25,476 Referee : Mr A Haynes.