Sheffield United scored twice in the final five minutes to snatch a draw.
Ledley celebrated his new Cardiff contract with a first-half goal
James Beattie's header from a Lee Hendrie corner gave the Blades the lead then Joe Ledley volleyed an equaliser.
Robbie Fowler converted a penalty when Chris Morgan fouled Roger Johnson, and after the break Jimmy Floyd Hasselbaink set up Gavin Rae who drilled home.
With five minutes left Chris Armstrong fired in a left-footer, and in a last minute goal-mouth melee Chris Armstong headed home from close range.
Sheffield United manager Bryan Robson:
"I hope the nature of the result is a turning point, but the main turning point has got to be for us to keep clean sheets. We can't keep conceding the goals we are doing.
"The first 45 minutes is as good a mixture of attacking play we've had. We caused Cardiff all sorts of problems and played some great stuff.
"I couldn't believe we came in at half-time 2-1 down. It was a huge task and the players showed great character, even the fans realised it wasn't a disjointed performance.
"The players deserved what they got, there's no way they deserved to lose."
Cardiff manager Dave Jones
"I've just berated my players for that final five minutes when really for 85 minutes we were outstanding, but we have to defend better.
"The second goal was the killer - when I look at the tape and see who switched off I'll strangle them.
"I can't fault the players otherwise, sometimes as a manager it's hard to swallow after a five-minute spell like that.
"But really we should not have allowed them back into the game, you have to kill matches off. We should not have to come here and score four goals to get a result, I can't keep that door shut."
Sheff Utd: Kenny, Bromby, Morgan, Cahill, Armstrong, Gillespie (Carney 25), Hendrie (Sharp 64), Tonge, Alan Quinn, Beattie, Stead (Shelton 64).
Subs Not Used: Kilgallon, Lucketti.
Goals: Beattie 18, Armstrong 85, Morgan 90.
Cardiff: Oakes, McNaughton, Loovens, Johnson, Capaldi, Parry, Rae, McPhail, Ledley, Fowler, Hasselbaink.
Subs Not Used: Turnbull, Purse, Whittingham, Green, Gunter.
Goals: Ledley 31, Fowler 45 pen, Rae 59.
Ref: Andy D'Urso (Essex).